Question

If f(x) = (x^2-x)/(x^2+2x).
Then find derivative of inverse of f(x).

Answer 1

first find the inverse, and then find its derivative OK....

Answer 2

inverse is so complicated to find :o

Answer 3

@Koikkara is an Engg. He will help you better.

Answer 4

Let \(\Large f(x)=y \implies f^{-1}f(x)=x= f^{-1}(y)\)
so, we need derivative of \( f^{-1}(y)\) or of x, which is
\(\huge \dfrac{dx}{dy}\)
use this :
\(\huge \dfrac{dx}{dy}=\dfrac{1}{\dfrac{dy}{dx}}\)
so, you'll need dy/dx which is easy, and just take the reciprocal.

Answer 5

And I shall differentiate whole equation w.r.t y ? :o How ?

Answer 6

no no....you'll first find dy/dx
by diff. w.r.t x only.
then since you required dx/dy, you will take the reciprocal

Answer 7

find f'(x)

Answer 8

So required derivative is 1/f'(x) ??

Answer 9

yes!

Answer 10

Ah Thanks !!

Answer 11

welcome ^_^