Differentiate: y= X^(e^x)

Question

anonymous · Answer

the derivate of e^x is e^x - you agree?
So use the power rule

anonymous · Answer

you must take the natural log of both sides

anonymous · Answer

then you must apply log rules and then solve for the y'

kinggeorge · Answer

Since $x$ is a variable, you do not want to use the power rule, as that's only used for constant exponents. However, you will need to put everything inside a natural log. So you get$$\ln(y)=\ln(x^{e^x})=e^x\ln(x)$$Now you can differentiate both sides using the product rule and implicit differentiation (for the function $y$).

kinggeorge · Answer

Once you've solved for $dy/dx$ in terms of $x$ and $y$, you can plug the equation $y=x^{e^x}$ in to get $dy/dx$ purely in terms of $x$.

austinl · Answer

Have you arrived at an answer yet? :)