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

1 Answer
Aug 9, 2016

#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)#