1. ## Here's another one

find d/dx e^x ln x

2. Originally Posted by kdstalnaker
find d/dx e^x ln x
Product rule:

$\displaystyle \frac{d}{dx} \{ f(x)g(x) \} = \frac{df}{dx}g(x)+f(x)\frac{dg}{dx}$

So here we let $\displaystyle f(x)=e^x$ and $\displaystyle g(x)=\ln(x)$, and
from here I'm sure you can complete the answer.

RonL

3. $\displaystyle e^x\ln x+\frac{1}{x}e^x=e^x(\ln x+\frac{1}{x})$