# What is the differentiation of log sin x ?

## Solution :

We have, y = log sin x

By using chain rule in differentiation,

Let u = sin x $$\implies$$ $$du\over dx$$ = cos x

And, y = log u $$\implies$$ $$dy\over du$$ = $$1\over u$$

Now, $$dy\over dx$$ = $$dy\over du$$ $$\times$$ $$du\over dx$$

$$\implies$$ $$dy\over dx$$ = $$1\over u$$ $$\times$$ cos x

$$\implies$$ $$dy\over dx$$ = $$1\over sin x$$ $$\times$$ cos x = cot x

Hence, the differentiation of log sin x with respect to x is cot x.

### Similar Questions

What is the differentiation of 1/log x ?

What is the differentiation of $$log x^2$$ ?

What is the Differentiation of x log x ?

What is the Differentiation of log log x ?