anonymous
  • anonymous
If f(x) = (x^2-x)/(x^2+2x). Then find derivative of inverse of f(x).
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
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goformit100
  • goformit100
first find the inverse, and then find its derivative OK....
anonymous
  • anonymous
inverse is so complicated to find :o
goformit100
  • goformit100
@Koikkara is an Engg. He will help you better.

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hartnn
  • hartnn
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.
anonymous
  • anonymous
And I shall differentiate whole equation w.r.t y ? :o How ?
hartnn
  • hartnn
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
hartnn
  • hartnn
find f'(x)
anonymous
  • anonymous
So required derivative is 1/f'(x) ??
hartnn
  • hartnn
yes!
anonymous
  • anonymous
Ah Thanks !!
hartnn
  • hartnn
welcome ^_^

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