Question

How do you find the derivative of `y=tan(arcsin(x))` ?

Answer 1

The answer is `sec^2(arcsin(x))*1/sqrt(1-x^2)`.

You have to recognize that the function is a composition of functions. Then you will understand that you will apply the chain rule: `(dy)/(dx)=f'(g(x))*g'(x)`.

So, let `f(x)=tan(x)` and `g(x)=arcsin(x)`. Then `f'(x)=sec^2(x)` and `g'(x)=1/sqrt(1-x^2)`.

Then proceed with substitutions into the chain rule.

The best study method is to write a reference sheet with all your basic derivatives and practicing the chain rule. The chain rule is heavily used in integration, so this is a MUST-KNOW topic!