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The Derivative of Inverse Function

The Derivative of Inverse Function. Example (1). Let f(x)=x 3 Find the value at x=8 of the derivative of f -1. Checking. Let’s check or answer by first finding the inverse function of f, then finding the derivative of this inverse function and lastly the value of this derivative at 8.

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The Derivative of Inverse Function

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  1. The Derivative of Inverse Function

  2. Example (1) Let f(x)=x3 Find the value at x=8 of the derivative of f-1

  3. Checking Let’s check or answer by first finding the inverse function of f, then finding the derivative of this inverse function and lastly the value of this derivative at 8.

  4. Why, then, we need a formula for the derivative of the inverse function?Why not just to proceed as shown in the previous slide? Because it is not always easy to find the inverse function!

  5. Example (2) Let f(x)=3cosx + 4x + 2 Assuming this function is one-to-one, Find the value at x=5 of the derivative of f-1

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