Question

cosx` * ctgx + cosx * ctgx`=

Answer 1

$Cos'(x)* ctg(x) + cos(x )* ctg'(x)=-sin(x)*\frac{ cos(x)}{sin(x)} -\frac{1}{sin^2(x)} *cos(x)=\\ =-cos(x)*(1+\frac{1}{sin^2(x)} )=-cos(x)*(2+ctg^2(x))$