Question

If f(x) = x+ tan x and g(x) is the inverse of f(x) then g'(x) is equal to..

Answer 1

@ganeshie8

Answer 2

aren't you trying to find the derivative of inverse at a particular point ?

Answer 3

answer is 1/(2+{g(x) - x}^2) and i have no clue

Answer 4

That doesn't seem right to me

Answer 5

at a particular point it would be easy na

Answer 6

maybe start with this :
\[f(g(x)) = x\]

Answer 7

Since it's the inverse I plugged it in to get:

\[x=g(x)+\tan g(x)\]
Then differentiate:

\[1=g'(x)+g'(x)\sec^2g(x) \]
\[g'(x)=\frac{1}{1+\sec^2 g(x)}\]

Answer 8

Well that's why I said it doesn't seem right idk depends on what kind of answer you're looking for I guess.

Answer 9

thanks i get it...
converting sec^2 g(x) to tan ^2 g(x)
then substituting tan^2 from the eqn f(g(x)) = x

Answer 10

Nice :)