# How do you differentiate f(x)=11xe^(2x) using the product rule?

Apr 17, 2018

$f ' \left(x\right) = 11 {e}^{2 x} \left(2 x + 1\right)$

#### Explanation:

The Product Rule tells us for two functions $f , g$ multiplied together, we take the derivative as follows:

$\left(f g\right) ' = f g ' + g f '$

So, for $f \left(x\right) = 11 x {e}^{2 x} ,$

$f ' \left(x\right) 11 x \frac{d}{\mathrm{dx}} {e}^{2 x} \cdot {e}^{2 x} \frac{d}{\mathrm{dx}} 11 x$

$\frac{d}{\mathrm{dx}} 11 x = 11$

$\frac{d}{\mathrm{dx}} {e}^{2 x} = 2 {e}^{2 x}$
S
Then,

$f ' \left(x\right) = 22 x {e}^{2 x} + 11 {e}^{2 x}$

Simplify:

$f ' \left(x\right) = 11 {e}^{2 x} \left(2 x + 1\right)$