Derivative of Inverse Function: Proof with Limits

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Where does the formula for the derivative of an inverse function come from? Here's an explanation using the limit definition of the derivative.

You can also prove this result using implicit differentiation, but limits are way more fun!
  1. Mu Prime Math
  2. #calculus
  3. #math
  4. #derivative
  5. #differentiate
  6. #inverse
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Great! I was struggling to understand my professor's demonstration, and this made things a lot clearer

孫傅康
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Thanks a lot I was having difficulties trying to derive this on my own

omergulcu
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you need the hypothesis f'(f^{-1}(x)) =/= 0 to justify bringing the limit into denominator. it's also probably better to write at the start that we are assuming f^{-1} is differentiable (although you did mention it during the derivation)

schweinmachtbree
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My calc teacher in high school just taught us this but didn't show the proof which she usually does. Thanks sm tho

bobmarley