Calculating Derivative – e to the power of a multiplication of x and ln – Exercise 6369

Exercise

Find the derivative of the following function:

f(x)=e^{x\ln x}

Final Answer

Show 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)

Have a question? Found a mistake? – Write a comment below!
Was it helpful? You can buy me a cup of coffee here, which will make me very happy and will help me upload more solutions!