void deriv705a (const range &r, char *task, char answ[][BUFSZ], char *src)
{
char buf[20][BUFSZ];
int a,bc,bd,c;
do {
a = rndr(r);
bc = rndr(r);
bd = rndr(r);
c = rndr(r);
} while (!(a!=0 && bc<bd && bc>0 && bd>0 && (bc*bc)%(bd*bd)!=0));
strcpy(task, "");
catprintf(task, "String(\"Найдите производную указанной функции:\")");
catprintf(task, "\ny(x)=((%s)/(%s)^2)*arcsin(%s)",
polynomial(buf[0],2,
1, chprintf(buf[1],"arctg(%s)", memb(buf[2], 1,a,1,1,"x",false)),
c, ""
),
polynomial(buf[3],2, a*a,"",1,"x^2"),
fraction(buf[4], bc,1,bd)
);
sprintf(src, "y(x)=((arctg(x/a))/((a^2+x^2)^2))*arcsin(b)");
sprintf(answ[0], "y(x)`=((%s)/((%s)^3))*arcsin(%s)",
polynomial(buf[0],2,
a,"",
-4,polynomial(buf[1],2,
1,chprintf(buf[2],"x*arctg(%s)", memb(buf[3],1,a,1,1,"x",false)),
-c,"x"
)
),
polynomial(buf[4],2, a*a,"", 1,"x^2"),
fraction(buf[5], bc,1,bd)
);
sprintf(answ[1], "y(x)`=((%s)/((%s)^4))*arcsin(%s)",
polynomial(buf[0],2,
a,"",
-2,polynomial(buf[1],2, 1,chprintf(buf[2],"x*arctg(%s)", memb(buf[3],1,a,1,1,"x",false)), -c,"x")
),
polynomial(buf[4],2, a*a,"", 1,"x^2"),
fraction(buf[5], bc,1,bd)
);
sprintf(answ[2], "y(x)`=((%s)/((%s)^3))*arcsin(%s)",
polynomial(buf[0],2,
a*a,"",
-4,polynomial(buf[1],2, 1,chprintf(buf[2],"x^2*arctg(%s)", memb(buf[3],1,a,1,1,"x",false)), -c,"x^2")
),
polynomial(buf[4],2, a*a,"", 1,"x^2"),
fraction(buf[5], bc,1,bd)
);
sprintf(answ[3], "y(x)`=((%s)/(sqrt(1-%s)*(%s)^4))",
polynomial(buf[0],2,
a,"",
-2,polynomial(buf[1],2, 1,chprintf(buf[2],"x*arctg(%s)", memb(buf[3],1,a,1,1,"x",false)), -c,"x")
),
fraction(buf[5], bc*bc,1,bd*bd),
polynomial(buf[4],2, a*a,"", 1,"x^2")
);
}
static int catrange (char **s, size_t *sz, size_t *len,
unsigned int lo, unsigned int hi, const char *sep)
{
int rc;
if (lo == hi)
rc = catprintf (s, sz, len, "%u%s", lo, sep);
else
rc = catprintf (s, sz, len, "%u-%u%s", lo, hi, sep);
return rc;
}
void deriv702a (const range &r, char *task, char answ[][BUFSZ], char *src)
{
char buf[20][BUFSZ];
int a, b, c, k;
do {
a = rndr(r);
b = rndr(r);
c = rndr(r);
k = rndr(r);
} while (!(a!=0 && b!=0 && k!=0 && k!=2 && k!=1));
strcpy(task, "");
catprintf(task, "String(\"Найдите производную указанной функции:\")");
catprintf(task, "\ny=(sin(%s)/(%s))*tg(%s)",
polynomial(buf[0],2, a,"x^2",b,""),
polynomial(buf[1],2, 1,"cos(x)^2", c,""),
memb(buf[2], 1,k,1,1,"pi", false)
);
sprintf(src, "y=(sin(a*x^2+b)/(cos(x)^2+c))*tg(pi/k)");
sprintf(answ[0], "y(x)`=tg(%s)*(((%s)*cos(%s)*(%s)+!(sin(2*x))*sin(%s))/((%s)^2))",
memb(buf[0], 1,k,1,1,"pi", false),
polynomial(buf[1],1, 2*a,"x"),
polynomial(buf[2],2, a,"x^2",b,""),
polynomial(buf[3],2, 1,"cos(x)^2", c,""),
polynomial(buf[4],2, a,"x^2",b,""),
polynomial(buf[5],2, 1,"cos(x)^2", c,"")
);
sprintf(answ[1], "y(x)`=tg(%s)*((%s)*cos(%s)-!(sin(2*x))*sin(%s))/((%s)^2))",
memb(buf[0], 1,k,1,1,"pi", false),
polynomial(buf[1],2, 1,"cos(x)^2", c,""),
polynomial(buf[2],2, a,"x^2",b,""),
polynomial(buf[3],2, a,"x^2",b,""),
polynomial(buf[4],2, 1,"cos(x)^2", c,"")
);
sprintf(answ[2], "y(x)`=(pi/(%s))*(%s)/((%s)^2))",
polynomial(buf[0],1, k*k,chprintf(buf[1],"cos(%s)^2", memb(buf[2], 1,k,1,1,"pi", false))),
polynomial(buf[3],2,
1,chprintf(buf[4], "sin(2*x)*sin(%s)", polynomial(buf[5],2, a,"x^2",b,"")),
-2*a, chprintf(buf[6], "x*(%s)*cos(%s)",
polynomial(buf[7],2, 1,"cos(x)^2", c,""),
polynomial(buf[8],2, a,"x^2", b,"")
)
),
polynomial(buf[9],2, 1,"cos(x)^2", c,"")
);
sprintf(answ[3], "y(x)`=tg(%s)*(((%s)*cos(%s)*(%s)-2*cos(x)*sin(%s))/((%s)^2))",
memb(buf[0], 1,k,1,1,"pi", false),
polynomial(buf[1],1, 2*a,"x"),
polynomial(buf[2],2, a,"x^2",b,""),
polynomial(buf[3],2, 1,"cos(x)^2", c,""),
polynomial(buf[4],2, a,"x^2",b,""),
polynomial(buf[5],2, 1,"cos(x)^2", c,"")
);
}
void deriv703a (const range &r, char *task, char answ[][BUFSZ], char *src)
{
char buf[20][BUFSZ];
int a, b, c;
do {
a = rndr(r);
b = rndr(r);
c = rndr(r);
} while (!(a!=0 && c!=0));
strcpy(task, "");
catprintf(task, "String(\"Найдите производную указанной функции:\")");
catprintf(task, "\ny=((%s)/sqrt(%s))*arctg(%d)",
polynomial(buf[0],2,
1,chprintf(buf[1], "arcsin(%s)", memb(buf[2], 1,a,1,1,"x", false)),
c,""
),
polynomial(buf[3],2, a*a,"", -1,"x^2"),
b
);
sprintf(src, "y(x)=((arcsin(x/a)+c)/sqrt(a^2-x^2))*arctg(b)");
sprintf(answ[0], "y(x)`=((%s)/sqrt((%s)^3))*arctg(%d)",
polynomial(buf[0],2,
a,chprintf(buf[1],"sqrt(%s)", polynomial(buf[2],2, a*a,"", -1,"x^2")),
-1,chprintf(buf[3],"x*(%s)", polynomial(buf[4],2, 1,chprintf(buf[5],"arcsin(%s)",memb(buf[6],1,a,1,1,"x")), c,""))
),
polynomial(buf[7],2, a*a,"", -1,"x^2"),
b
);
sprintf(answ[1], "y(x)`=((%s)/sqrt((%s)^3))*arctg(%d)",
polynomial(buf[0],2,
a,chprintf(buf[1],"sqrt(%s)", polynomial(buf[2],2, a*a,"", -1,"x^2")),
-1,chprintf(buf[3],"x*(%s)", polynomial(buf[4],2, 1,chprintf(buf[5],"arcsin(%s)",memb(buf[6],1,a,1,1,"x")), c,""))
),
polynomial(buf[7],2, a*a,"", -1,"x^2"),
b
);
sprintf(answ[2], "y(x)`=(%s)/(%s)",
polynomial(buf[0],2,
a,chprintf(buf[1],"sqrt(%s)", polynomial(buf[2],2, a*a,"", -1,"x^2")),
-1,chprintf(buf[3],"x*(%s)", polynomial(buf[4],2, 1,chprintf(buf[5],"arcsin(%s)",memb(buf[6],1,a,1,1,"x")), c,""))
),
polynomial(buf[7],2, a*a*(1+b*b),"", -(1+b*b),"x^2")
);
sprintf(answ[3], "y(x)`=(%s)/(%s)",
polynomial(buf[0],2,
a,chprintf(buf[1],"sqrt(%s)", polynomial(buf[2],2, a*a,"", -1,"x^2")),
2,chprintf(buf[3],"x*(%s)", polynomial(buf[4],2, 1,chprintf(buf[5],"arcsin(%s)",memb(buf[6],1,a,1,1,"x")), c,""))
),
polynomial(buf[7],2, a*a*(1+b*b),"", -(1+b*b),"x^2")
);
}
void deriv704a (const range &r, char *task, char answ[][BUFSZ], char *src)
{
char buf[20][BUFSZ];
int a, n;
do {
a = rndr(r);
n = rndr(r);
} while (!(a!=0 && n>1));
strcpy(task, "");
catprintf(task, "String(\"Найдите производную указанной функции:\")");
catprintf(task, "\ny=(%s)/sqrt(%s)",
memb(buf[0], 1,1,n,1, chprintf(buf[1],"arccos(%s)", memb(buf[2], 1,a,1,1, "x", false)), false),
polynomial(buf[3],2, a*a,"", -1,"x^2")
);
sprintf(src, "y(x)=arccos(x/a)^n/sqrt(a^2-x^2)");
sprintf(answ[0], "y(x)`=((%s)*(%s))/sqrt((%s)^3)",
memb(buf[0], 1,1,n-1,1, chprintf(buf[1],"arccos(%s)", memb(buf[2], 1,a,1,1, "x", false)), false),
polynomial(buf[3],2,
1,chprintf(buf[4], "x*arccos(%s)", memb(buf[5], 1,a,1,1,"x", false)),
-n, chprintf(buf[6], "sqrt(%s)", polynomial(buf[7],2,a*a,"",-1,"x^2"))
),
polynomial(buf[7],2, a*a,"", -1,"x^2")
);
sprintf(answ[1], "y(x)`=(%s)/(%s)",
polynomial(buf[0],2,
2*a, chprintf(buf[1], "x*(%s)", memb(buf[2], 1,1,n,1, chprintf(buf[3],"arccos(%s)", memb(buf[4],1,a,1,1,"x", false)), false)),
-n,chprintf(buf[5], "sqrt(%s)*(%s)",
polynomial(buf[6],2, a*a,"", -1,"x^2"),
memb(buf[7], 1,1,n-1,1, chprintf(buf[8],"arccos(%s)", memb(buf[9],1,a,1,1,"x", false)), false)
)
),
polynomial(buf[10],2, a*a,"", -1,"x^2")
);
sprintf(answ[2], "y(x)`=((%s)*(%s))/(%s)",
memb(buf[0], 1,1,n-1,1, chprintf(buf[1], "arccos(%s)", memb(buf[2], 1,a,1,1,"x", false)), false),
polynomial(buf[3],2,
n,chprintf(buf[4],"sqrt(%s)", polynomial(buf[5],2, a*a,"", -1,"x^2")),
-1,chprintf(buf[6],"x*arccos(%s)", memb(buf[7], 1,a,1,1,"x", false))
),
memb(buf[8], a,1,1,1, chprintf(buf[9],"sqrt((%s)^3)", polynomial(buf[10],2,a*a,"",-1,"x^2")), false)
);
sprintf(answ[3], "y(x)`=((%s)*(%s))/(%s)",
memb(buf[0], 1,1,n-1,1, chprintf(buf[1], "arccos(%s)", memb(buf[2], 1,a,1,1,"x", false)), false),
polynomial(buf[3],2,
-n*a, polynomial(buf[5],2, a*a,"", -1,"x^2"),
1,chprintf(buf[6],"x*arccos(%s)", memb(buf[7], 1,a,1,1,"x", false))
),
polynomial(buf[10],2,a*a,"",-1,"x^2")
);
}
void deriv707a (const range &r, char *task, char answ[][BUFSZ], char *src)
{
char buf[20][BUFSZ];
int a, b, c;
do {
a = rndr(r);
b = rndr(r);
c = rndr(r);
} while (!(a!=0 && b>1));
char arctgxac[BUFSZ];
polynomial(arctgxac,2,
1,chprintf(buf[0],"arctg(%s)", memb(buf[1], 1,a,1,1, "x", false)),
c,""
);
char xarctgxac[BUFSZ];
sprintf(xarctgxac, "x*(%s)", arctgxac);
char a2x2[BUFSZ];
polynomial(a2x2,2, a*a,"",1,"x^2");
strcpy(task, "");
catprintf(task, "String(\"Найдите производную указанной функции:\")");
catprintf(task, "\ny(x)=((%s)/sqrt(%s))*ln(%d)", arctgxac, a2x2, b);
sprintf(src, "y(x)=((arctg(x/a)+c)/sqrt(a*x^2+b))*ln(b)");
sprintf(answ[0], "y(x)`=((%s)/sqrt((%s)^3))*ln(%d)",
polynomial(buf[0],2, a,"", -1,xarctgxac),
a2x2,
b
);
sprintf(answ[1], "y(x)`=((%s)/sqrt((%s)^3))*ln(%d)",
polynomial(buf[0],2, a,"", -2,xarctgxac),
a2x2,
b
);
sprintf(answ[2], "y(x)`=((%s)/(%s))*ln(%d)",
polynomial(buf[0],2, a,"", -1,xarctgxac),
a2x2,
b
);
sprintf(answ[3], "y(x)`=((%s)/(%s))",
polynomial(buf[0],2, a,"", -1,xarctgxac),
polynomial(buf[1],1, b,a2x2)
);
}
void deriv708a (const range &r, char *task, char answ[][BUFSZ], char *src)
{
char buf[20][BUFSZ];
int a, b, p, c;
do {
a = rndr(r);
b = rndr(r);
p = rndr(r);
c = rndr(r);
} while (!(a>0 && b>0));
char ax2b[BUFSZ];
polynomial(ax2b,2, a,"x^2", b,"");
char lnax2b[BUFSZ];
sprintf(lnax2b, "ln(%s)", ax2b);
strcpy(task, "");
catprintf(task, "String(\"Найдите производную указанной функции:\")");
catprintf(task, "\ny(x)=((%s)/sqrt(%s))*cos(%d)",
polynomial(buf[0],2, 1,lnax2b, c,""),
ax2b,
p
);
sprintf(src, "y(x)=((ln(a*x^2+b)+c)/sqrt(a*x^2+b))*cos(p)");
sprintf(answ[0], "y(x)`=((%s)/sqrt((%s)^3))*cos(%d)",
polynomial(buf[0],1, a,chprintf(buf[1],"x*(%s)", polynomial(buf[2],2, 2-c,"", -1,lnax2b))),
ax2b,
p
);
sprintf(answ[1], "y(x)`=((%s)/sqrt((%s)^3))*cos(%d)",
polynomial(buf[0],1, a,chprintf(buf[1],"x^2*(%s)", polynomial(buf[2],2, 1-c,"", -1,lnax2b))),
ax2b,
p
);
sprintf(answ[2], "y(x)`=((%s)/sqrt((%s)^3))*sin(%d)",
polynomial(buf[0],1, a,chprintf(buf[1],"x*(%s)", polynomial(buf[2],2, c-2,"", 1,lnax2b))),
ax2b,
p
);
sprintf(answ[3], "y(x)`=((%s)/(%s))*sin(%d)",
polynomial(buf[0],1, a,chprintf(buf[1],"x^2*(%s)", polynomial(buf[2],2, 1,lnax2b, -2+c,""))),
ax2b,
p
);
}
void deriv415a (const range &r, char *task, char answ[][BUFSZ], char *src)
{
char buf[20][BUFSZ];
int a, b, c;
do {
a = rndr(r);
b = rndr(r);
c = rndr(r);
} while (!(a>1 && b>0));
strcpy(task, "");
catprintf(task, "String(\"Найдите производную указанной функции:\")");
catprintf(task, "\ny(x)=arcsin(sqrt(%d/x))+arctg(%d)", b,c);
sprintf(answ[0], "y(x)`=-(%s/(2*x*sqrt(%s)))",fraction(buf[0],1,b,1),polynomial(buf[1],2,1,"x",-b,""));
sprintf(answ[1], "y(x)`=(%s)/(2*sqrt(%s))",polynomial(buf[0],1,b,"x"),polynomial(buf[1],2,1,"x",-b,""));
sprintf(answ[2], "y(x)`=(%d)/(2*x^2*sqrt(1-(%d)/x))+arctg(%d)",-b,b,c);
sprintf(answ[0], "y(x)`=-(%s/(2*x*sqrt(%s)))+(%s)",fraction(buf[0],1,b,1),polynomial(buf[1],2,1,"x",-b,""), fraction(buf[2],1,1,1+c*c));
}
void deriv413a (const range &r, char *task, char answ[][BUFSZ], char *src)
{
char buf[20][BUFSZ];
int a, b, c;
do {
a = rndr(r);
b = rndr(r);
c = rndr(r);
} while (!(a>1 && b!=0));
strcpy(task, "");
catprintf(task, "String(\"Найдите производную указанной функции:\")");
catprintf(task, "\ny(x)=sin(log(%d,%s))+cos(%d)", a,polynomial(buf[0],1,b,"x"),c);
sprintf(answ[0], "y(x)`=cos(log(%d,%d))/(x*ln(%d))",a,b,a);
sprintf(answ[1], "y(x)`=(cos(log(%d,%d))/((%s)*ln(%d)))+sin(%d)",a,b,polynomial(buf[0],1,b,"x"),a,c);
sprintf(answ[2], "y(x)`=%s", polynomial(buf[0],1,b,chprintf(buf[1],"cos(1/((%s)*ln(%d)))", polynomial(buf[2],1,b,"x"),a)));
sprintf(answ[3], "y(x)`=(cos(log(%d,%d))/(x*ln(%d)))-sin(%d)", a,b,a,c);
}
void deriv701a (const range &r, char *task, char answ[][BUFSZ], char *src)
{
char buf[20][BUFSZ];
int a, b, m, n, c, d;
do {
a = rndr(r);
b = rndr(r);
c = rndr(r);
d = rndr(r);
m = rndr(range(2, 4));
n = rndr(range(2, 4));
} while (!(c>0 && d>0 && m*n>2 && a!=b && a!=0 && b!=0));
strcpy(task, "");
catprintf(task, "String(\"Найдите производную указанной функции:\")");
catprintf(task, "\ny=(%s)/(%s)",
memb(buf[0], 1,1,m,1, polynomial(buf[1],2, a,"x", b,""), false),
memb(buf[2], 1,1,1,n, polynomial(buf[3],2, c,"x", d,""), false)
);
sprintf(src, "y=((a*x+b)^m)/root(n,c*x+d)");
sprintf(answ[0], "y(x)`=((%s)*(%s))/(%s)",
memb(buf[0], 1,1,m-1,1, polynomial(buf[1],2, a,"x",b,""), false),
polynomial(buf[2],2, a*c*(m*n-1),"x", a*m*n*d-c*b,""),
memb(buf[3], n,1,n+1,n, polynomial(buf[4],2, c,"x",d,""), false)
);
sprintf(answ[1], "y(x)`=((%s)*(%s))/(%s)",
memb(buf[0], m,1,m-1,1, polynomial(buf[1],2, a,"x",b,""), false),
polynomial(buf[2],2, a*c,"x", -c*b,""),
memb(buf[3], n,1,2,n, polynomial(buf[4],2, c,"x",d,""), false)
);
sprintf(answ[2], "y(x)`=((%s)*(%s))/(%s)",
memb(buf[0], m,1,m-1,1, polynomial(buf[1],2, a,"x",b,""), false),
polynomial(buf[2],2, m*a-c,"x", d*b,""),
memb(buf[3], n,1,n+1,n, polynomial(buf[4],2, c,"x",d,""), false)
);
sprintf(answ[3], "y(x)`=((%s)*(%s))/(%s)",
memb(buf[0], 1,1,m-1,1, polynomial(buf[1],2, a,"x",b,""), false),
polynomial(buf[2],2, a*c,"x", a*d-c*b,""),
memb(buf[3], n,1,2,n, polynomial(buf[4],2, c,"x",d,""), false)
);
}
char *idset_encode (const struct idset *idset, int flags)
{
char *str = NULL;
size_t strsz = 0;
size_t strlength = 0;
int count;
if (validate_idset_flags (flags, IDSET_FLAG_BRACKETS
| IDSET_FLAG_RANGE) < 0)
return NULL;
if (!idset) {
errno = EINVAL;
return NULL;
}
if ((flags & IDSET_FLAG_BRACKETS)) { // add open brace, if requested
if (catprintf (&str, &strsz, &strlength, "[") < 0)
goto error;
}
if ((flags & IDSET_FLAG_RANGE))
count = encode_ranged (idset, &str, &strsz, &strlength);
else
count = encode_simple (idset, &str, &strsz, &strlength);
if (count < 0)
goto error;
if ((flags & IDSET_FLAG_BRACKETS) && count > 1) { // add close brace
if (catprintf (&str, &strsz, &strlength, "]") < 0)
goto error;
}
if (!str) {
if (!(str = strdup ("")))
goto error;
}
if (count <= 1 && str[0] == '[') // no braces for singletons
memmove (str, str + 1, strlength); // moves '\0' too
return str;
error:
free (str);
errno = ENOMEM;
return NULL;
}
void deriv414a (const range &r, char *task, char answ[][BUFSZ], char *src)
{
char buf[20][BUFSZ];
int a, b, c;
do {
a = rndr(r);
b = rndr(r);
c = rndr(r);
} while (!(a>1 && b!=0));
strcpy(task, "");
catprintf(task, "String(\"Найдите производную указанной функции:\")");
catprintf(task, "\ny(x)=cos((%d)^(%s))^2+tg(%d)", a,polynomial(buf[0],1,b,"x"),c);
char blna[BUFSZ]; polynomial(blna,1, b,chprintf(buf[0],"ln(%d)",a));
char abx[BUFSZ]; sprintf(abx,"(%d)^(%s)", a, polynomial(buf[0],1,b,"x"));
sprintf(answ[0], "y(x)`=(-sin(2*%s))*.(%s)*.(%s)",abx,abx,blna);
sprintf(answ[1], "y(x)`=2*(cos(%s))*.(%s)+tg(%d)",abx,blna,c);
sprintf(answ[2], "y(x)`=(sin(%s)^2)*.(%s)+1/cos(%d)^2",abx,blna,c);
sprintf(answ[3], "y(x)`=2*(cos(%s))*.(sin(%s)^2)*.(%s)",abx,abx,blna);
}
void deriv412a (const range &r, char *task, char answ[][BUFSZ], char *src)
{
char buf[20][BUFSZ];
int a, b, c;
do {
a = rndr(r);
b = rndr(r);
c = rndr(r);
} while (!(a>1 && b!=0));
char bx[BUFSZ];
polynomial(bx,1, b,"x");
strcpy(task, "");
catprintf(task, "String(\"Найдите производную указанной функции:\")");
catprintf(task, "\ny(x)=(%d)^arctg(%s)+tg(%d)^2", a,bx,c);
sprintf(src, "y(x)=a^arctg(b*x)+tg(c)^2");
sprintf(answ[0], "y(x)`=(%d)^arctg(%s)*.!(ln(%d))*.(%d/(%s))", a,bx,a,b,polynomial(buf[0],2,1,"",b*b,"x^2"));
sprintf(answ[1], "y(x)`=(%d)^arctg(%s)*.!(ln(%d))+tg(%d)^2", a,bx,a,c);
sprintf(answ[2], "y(x)`=(%d)^(%d/(%s))*.!(ln(%d))+(2*tg(%d))/(cos(%d)^2)", a,b,polynomial(buf[0],2,1,"",b*b,"x^2"),a,c,c);
sprintf(answ[3], "y(x)`=arctg(%s)*(%d)^(arctg(%s)-1)*.(%d/(%s))", bx,a,bx,b,polynomial(buf[0],2,1,"",b*b,"x^2"));
}
void deriv410a (const range &r, char *task, char answ[][BUFSZ], char *src)
{
char buf[20][BUFSZ];
int a, b, c;
do {
a = rndr(r);
b = rndr(r);
c = rndr(r);
} while (!(a>1 && b!=0 && c>1));
char bx[BUFSZ];
polynomial(bx,1, b,"x");
strcpy(task, "");
catprintf(task, "String(\"Найдите производную указанной функции:\")");
catprintf(task, "\ny(x)=(%d)^ctg(%s)+1/sin(%d)", a,bx,c);
sprintf(src, "y(x)=a^ctg(b*x)+1/sin(c)");
sprintf(answ[0], "y(x)`=(%d)^tg(%s)*.!(ln(%d))*.(%d/sin(%s)^2)", a,bx,a,-b,bx);
sprintf(answ[1], "y(x)`=(%d)^tg(%s)*.!(ln(%d))*.(%d/cos(%s)^2)+1/sin(%d)", a,bx,a,b,bx,c);
sprintf(answ[2], "y(x)`=(%d)^tg(%s)*.!(ln(%d))*.(%d/sin(%s)^2)-(cos(%d)/sin(%d)^2)", a,bx,a,-b,bx,c,c);
sprintf(answ[3], "y(x)`=ctg(%s)*(%d)^(tg(%s)-1)*.(%d/sin(%s)^2)", bx,a,bx,b,bx);
}
void deriv706a (const range &r, char *task, char answ[][BUFSZ], char *src)
{
char buf[20][BUFSZ];
int a, n;
do {
a = rndr(r);
n = rndr(r);
} while (!(a!=0 && n>0));
strcpy(task, "");
catprintf(task, "String(\"Найдите производную указанной функции:\")");
catprintf(task, "\ny(x)=arctg(%s)/(%s)",
memb(buf[0], 1,a,1,1,"x", false),
memb(buf[1], 1,1,n,1, polynomial(buf[2],2, a*a,"",1,"x^2"), false)
);
sprintf(src, "y(x)=arctg(x/a)/(a^2+x^2)^n");
char xarctg[BUFSZ];
sprintf(xarctg, "x*arctg(%s)", memb(buf[0], 1,a,1,1, "x", false));
sprintf(answ[0], "y(x)`=(%s)/(%s)",
polynomial(buf[0],2, a,"", -2*n,xarctg),
memb(buf[1], 1,1,n+1,1, polynomial(buf[2],2, a*a,"", 1,"x^2"), false)
);
sprintf(answ[1], "y(x)`=(%s)/(%s)",
polynomial(buf[0],2, a*a,"", -4*n,xarctg),
memb(buf[1], 1,1,n+1,1, polynomial(buf[2],2, a*a,"", 1,"x^2"), false)
);
sprintf(answ[2], "y(x)`=(%s)/(%s)",
polynomial(buf[0],2, a,polynomial(buf[1],2, a*a,"", 1,"x^2"), -2*n,xarctg),
memb(buf[2], 1,1,n,1, polynomial(buf[3],2, a*a,"", 1,"x^2"), false)
);
sprintf(answ[3], "y(x)`=(%s)/(%s)",
polynomial(buf[0],2, a*a,"", -2*n,xarctg),
memb(buf[1], 1,1,n,1, polynomial(buf[2],2, a*a,"", 1,"x^2"), false)
);
}
/* Return value: count of id's in set, or -1 on failure.
* N.B. if count is more than INT_MAX, return value is INT_MAX.
*/
static int encode_simple (const struct idset *idset,
char **s, size_t *sz, size_t *len)
{
int count = 0;
unsigned int id;
id = vebsucc (idset->T, 0);
while (id != idset->T.M) {
int next = vebsucc (idset->T, id + 1);
char *sep = next == idset->T.M ? "" : ",";
if (catprintf (s, sz, len, "%d%s", id, sep) < 0)
return -1;
if (count < INT_MAX)
count++;
id = next;
}
return count;
}