Question

f(x) = √(cotx.x³) dx

Answer 1

$$f(x)=\sqrt{\cot x\cdot x^3}$$

$${df \over dx}={1 \over 2\sqrt{\cot x\cdot x^3}}(-{x^3 \over \sin^2x}+3x^2\cot x)=$$

$$={\sqrt{x}(3\sin x\cos x-x) \over 2\sqrt{\cos x\sin ^3x}}$$