Question

Find the derivative r = cos x cot x.

Answer 1

r = cos x cot x

\(\frac{dr}{dx}\) = cos x \(\frac{d}{dx}\) cot x + (\(\frac{d}{dx}\)cos x) cot x

 = cos x (- cosec²x) - sin x cot x

 = - cos x. cosec² x - sin x\(\frac{cosx}{sin x}\) 

 = - cos x (cosec²x + 1)