# How do you differentiate  f(x)=(e^x+1)*(x+1)*sqrt(x^2-3) using the product rule?

$f ' \left(x\right) = {e}^{x} \cdot \left(x + 1\right) \cdot \sqrt{{x}^{2} - 3} + \left({e}^{x} + 1\right) \cdot \sqrt{{x}^{2} - 3} + \frac{\left({e}^{x} + 1\right) \cdot \left(x + 1\right) \cdot x}{\sqrt{{x}^{2} - 3}}$
$f \left(x\right) = u \cdot v \cdot s$
$f ' \left(x\right) = u ' \cdot v \cdot s + u \cdot v ' \cdot s + u \cdot v \cdot s '$
$f \left(x\right) = \left({e}^{x} + 1\right) \cdot \left(x + 1\right) \cdot \sqrt{{x}^{2} - 3}$
$f ' \left(x\right) = {e}^{x} \cdot \left(x + 1\right) \cdot \sqrt{{x}^{2} - 3} + \left({e}^{x} + 1\right) \cdot \sqrt{{x}^{2} - 3} + \frac{\left({e}^{x} + 1\right) \cdot \left(x + 1\right) \cdot x}{\sqrt{{x}^{2} - 3}}$