How do you differentiate tan(sin x)?

1 Answer
Apr 28, 2018

sec^2(sinx)cosx

Explanation:

Given: d/dx(tan(sinx)).

Here, let y=tan(sinx).

Use the chain rule, which states that,

dy/dx=dy/(du)*(du)/dx

Let u=sinx,:.(du)/dx=cosx.

Then y=tanu,dy/(du)=sec^2u.

So, combining our results, we get:

dy/dx=sec^2u*cosx

Substituting back u=sinx, we get:

dy/dx=sec^2(sinx)*cosx

=sec^2(sinx)cosx