Question

Derive (cos(x).cotg(x))/(sec(x)-cos(x)).

Answer 1

$f(x)= \frac{cosx.cotgx}{secx-cosx} \\ \\ f(x)= \frac{cosx. \frac{cosx}{senx} }{ \frac{1}{cosx}-cosx } \\ \\ f(x)= \frac{ \frac{cos^2x}{senx} }{ \frac{1-cos^2x}{cosx} } \\ \\ f(x)= \frac{cos^3x}{sen^3x} \\ \\ f(x)=cotg^3x \\ \\ f'(x)=-3cossec^2x.cotg^2x$