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 \(\cos{x}\).
\[{e}^{x}\sin{x}+{e}^{x}\cos{x}\]

Done
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