# How do you find the first and second derivative of xlnx^2?

Mar 7, 2018

See below.

#### Explanation:

First use properties of logarithms to rewrite

$f \left(x\right) = x \ln {x}^{2} = 2 x \ln x$

Now use the product rule

$f ' \left(x\right) = 2 \ln x + 2$

$f ' ' \left(x\right) = \frac{2}{x}$