Exercise
Find the derivative of the inverse of the following function:
f(x)=\ln x
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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