# How do you differentiate g(x) = xsqrt(1-e^(2x)) using the product rule?

Jun 18, 2018

g'(x)=sqrt(1-e^(2x))-(x*e^(2x))/(sqrt(1-e^(2x))

#### Explanation:

After the product and the chain rule we get

$g ' \left(x\right) = \sqrt{1 - {e}^{2 x}} + x + \frac{1}{2} \cdot {\left(1 - {e}^{2 x}\right)}^{- \frac{1}{2}} \cdot \left(- {e}^{2 x}\right) \cdot 2$
this simplifies to

$g ' \left(x\right) = \sqrt{1 - {e}^{2 x}} - \frac{x \cdot {e}^{2 x}}{\sqrt{1 - {e}^{2 x}}}$