Problem of the Week

Updated at Nov 17, 2014 8:42 AM

How can we find the derivative of \(x\sin{x}\)?

Below is the solution.



\[\frac{d}{dx} x\sin{x}\]

1
Use Product Rule to find the derivative of \(x\sin{x}\). The product rule states that \((fg)'=f'g+fg'\).
\[(\frac{d}{dx} x)\sin{x}+x(\frac{d}{dx} \sin{x})\]

2
Use Power Rule: \(\frac{d}{dx} {x}^{n}=n{x}^{n-1}\).
\[\sin{x}+x(\frac{d}{dx} \sin{x})\]

3
Use Trigonometric Differentiation: the derivative of \(\sin{x}\) is \(\cos{x}\).
\[\sin{x}+x\cos{x}\]

Done
Cymath foriOSAndroid