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Calculating Derivative – ln in ln – Exercise 6355

Exercise

Find the derivative of the following function:

f(x)=\ln\ln x

Final Answer


f'(x)=\frac{1}{x\ln x}

Solution

f(x)=\ln\ln x

Using Derivative formulas and chain rule in Derivative Rules, we get the derivative:

f'(x)=\frac{1}{\ln x}\cdot\frac{1}{x}=

One can simplify the derivative:

=\frac{1}{x\ln x}

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