## anonymous 4 years ago Let f(x)=10x+(arctanx)^2+2. If g(x) = f-1(x) <- inverse. If g is the inverse function of f, then find the value of g'(2) so far I have got the derivative of g(x) f'(y) = 10y'+2(arctany)y'/1+y^2 and I can't figure out what to do with the y^2

1. dumbcow

$g'(2) = \frac{1}{f'(g(2))}$ $f'(x) = 10 + \frac{2 \tan^{-1} x}{1+x^{2}}$ g(2) is the solution to f(x) = 2 $10x + (\tan^{-1} x)^{2} +2 = 2$ $10x +(\tan^{-1} x)^{2} = 0$ x = 0 http://www.wolframalpha.com/input/?i=10x+%2B+arctan%28x%29%5E2+%3D+0 $f'(0) = 10 + 2\tan^{-1} 0 / 1+0= 10$ $g'(2) = \frac{1}{10}$

2. anonymous

thank you so much!

3. dumbcow

no problem... sorry i kinda got lost trying to follow your work, i like to just keep everything in terms of x

4. anonymous

It was my fault should've made it more clearer :(

5. dumbcow

you took the derivative correctly though just looks like you used implicit differentiation ?

6. anonymous

yes I did implicit differentiation, but that just got me more confused. Your method was much easier to understand the question :)

7. dumbcow

:)