# Problem of the Week

## Updated at Nov 4, 2013 12:07 PM

How would you differentiate $${e}^{x}\sin{x}$$?

Below is the solution.

$\frac{d}{dx} {e}^{x}\sin{x}$

 1 Use Product Rule to find the derivative of $${e}^{x}\sin{x}$$. The product rule states that $$(fg)'=f'g+fg'$$.$(\frac{d}{dx} {e}^{x})\sin{x}+{e}^{x}(\frac{d}{dx} \sin{x})$2 The derivative of $${e}^{x}$$ is $${e}^{x}$$.${e}^{x}\sin{x}+{e}^{x}(\frac{d}{dx} \sin{x})$3 Use Trigonometric Differentiation: the derivative of $$\sin{x}$$ is $$\cos{x}$$.${e}^{x}\sin{x}+{e}^{x}\cos{x}$Donee^x*sin(x)+e^x*cos(x)