Exercise
Find the derivative of the following function:
f(x)=e^{x\ln x}
Final Answer
Solution
f(x)=e^{x\ln x}
Using Derivative formulas and the multiplication rule and chain rule in Derivative Rules, we get the derivative:
f'(x)=e^{x\ln x}\cdot (\ln x+x\cdot\frac{1}{x})=
One can simplify the derivative using logarithm rules:
=e^{\ln x^x}\cdot (\ln x+1)=
=x^x\cdot (\ln x+1)
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