Question

Let f(x)=(tan^(−1)x)^6. Find f′(x)

Answer 1

i take it this is
\[(\tan^{-1}(x))^6\]

Answer 2

http://www.wolframalpha.com/input/?i=diff+%28%28tan%5E%28 −1%29x%29%29%5E6

Answer 3

then you need the chain rule
you will get
\[6(\tan^{-1}(x))^5\times \frac{d}{dx}\tan^{-1}(x)\]

Answer 4

and
\[\frac{d}{dx}\tan^{-1}(x)=\frac{1}{x^2+1}\] so put it together and you are done