Question

How do you find the derivative of `f(x)= x^2*tan^-1 x`?

Answer 1

`f'(x)=2xtan^-1x+x^2/(1+x^2)`

Explanation:

We have to use the product rule, which states that for a function `f(x)=g(x)*h(x)`, the derivative is equal to `f'(x)=g'(x)*h(x)+g(x)*h'(x)`. Here, we see that:

`f'(x)=d/dx(x^2)*tan^-1x+x^2*d/dx(tan^-1x)`

`f'(x)=2x*tan^-1x+x^2*(1/(1+x^2))`

`f'(x)=2xtan^-1x+x^2/(1+x^2)`