# Problem of the Week

## Updated at Oct 14, 2013 8:37 AM

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

Below is the solution.

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

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