Question

Differentiate sin(log sin x) ?

Answer 1

Let y = sin (log sin x)

Differentiate it with respect to x We get,

`(dy)/(dx)=d/(dx)sin (log sin x)`

`=cos (log sin x)d/(dx)(log sin x)`       [Using chain rule]

`=cos (log sin x)xx1/(sin x)d/(dx)sin x`         [Using chain rule]

`=cos (log sin x)(cos x)/(sin x)`

`=cos (log sin x) cot x`

Hence, `d/(dx)sin (log sin x) = cos (log sin x) cot x`