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

Question

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

anonymous · Answer

@ganeshie8

ganeshie8 · Answer

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

anonymous · Answer

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

empty · Answer

That doesn't seem right to me

anonymous · Answer

at a particular point it would be easy na

ganeshie8 · Answer

maybe start with this :
$$f(g(x)) = x$$

empty · Answer

Since it's the inverse I plugged it in to get:

$$x=g(x)+\tan g(x)$$
Then differentiate:

$$1=g'(x)+g'(x)\sec^2g(x) $$
$$g'(x)=\frac{1}{1+\sec^2 g(x)}$$

empty · Answer

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

anonymous · Answer

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

ganeshie8 · Answer

Nice :)