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 \(-\csc{x}\cot{x}\).
\[{e}^{x}\csc{x}-{e}^{x}\csc{x}\cot{x}\]

Done
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