# What is the derivative of f(x) = -5 e^{xcos x}?

I found: $f ' \left(x\right) = - 5 {e}^{x \cos \left(x\right)} \times \left[\cos \left(x\right) - x \sin \left(x\right)\right]$
Here I would use the Chain Rule to deal first with $e$ (red) and then with the exponent (blue where you need the Product Rule):
$f ' \left(x\right) = - 5 \textcolor{red}{{e}^{x \cos \left(x\right)}} \times \textcolor{b l u e}{\left[1 \cdot \cos \left(x\right) - x \cdot \sin \left(x\right)\right]}$