How do I find the derivatives of this function?

Question

f(x) = tan^−1(x^2) this is an inverse function.

f ' (x) = ?

f '' (x) = ?

Answer 1

Step 1 :

The function is .

Apply derivative on each side with respect to x.

The first derivative is

Step 2 :

Differentiate with respect to x.

Apply quotient rule of derivatives :

The second derivative is

Solution :

The first derivative is

The second derivative is