Question

How do you differentiate `f(x)= x^2*tan^-1 x`?

Answer 1

The answer is `f'(x)=x^2/(1+x^2)+2x tan^{-1}(x)`

Explanation:

This follows from the Product Rule `d/dx(g(x)h(x))=g(x)h'(x)+g'(x)h(x)` (with `g(x)=x^2` and `h(x)=tan^{-1}(x)`), the Power Rule `d/dx(x^(n))=nx^(n-1)`, and the derivative of inverse tangent `d/dx(tan^{-1}(x))=1/(1+x^2)`.