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

Show final answer

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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