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Calculating Derivative – Computing a derivative of an inverse function – Exercise 2086

Exercise

Find the derivative of the inverse of the following function:

f(x)=\ln x

Final Answer


(f^{-1})'(x)=e^x

Solution

Given the function:

f(x)=\ln x

Its inverse function is

f^{-1}(x)=e^x

We use the formula to find the derivative of the inverse function and get:

(f^{-1})'(x)=(e^x)'=

=\frac{1}{(\ln (e^x))'}=

=\frac{1}{\frac{1}{e^x}}=e^x

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