# What is the derivative of y=xlnx?

Feb 3, 2015

#### Answer:

$\ln x + 1$ evaluated via Product Rule

#### Explanation:

The answer is: $y ' = 1 \cdot \ln x + x \cdot \frac{1}{x} = \ln x + 1$.

This is because the theorem of derivative of product (Product Rule) says:

$y = f \left(x\right) \cdot g \left(x\right) \Rightarrow y ' \left(x\right) = f ' \left(x\right) \cdot g \left(x\right) + f \left(x\right) \cdot g ' \left(x\right)$ where

$f \left(x\right) = x$

$f ' \left(x\right) = 1$

$g \left(x\right) = \ln x$

$g ' \left(x\right) = \frac{1}{x}$