Problem of the Week

Updated at Apr 16, 2018 10:34 AM

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Apr 16, 2018

To get more practice in calculus, we brought you this problem of the week:

How would you differentiate \(8x\sin{x}\)?

Check out the solution below!

\[\frac{d}{dx} 8x\sin{x}\]

: \(\frac{d}{dx} cf(x)=c(\frac{d}{dx} f(x))\)

\[8(\frac{d}{dx} x\sin{x})\]

to find the derivative of \(x\sin{x}\)
The product rule states that \((fg)'=f'g+fg'\)

\[8((\frac{d}{dx} x)\sin{x}+x(\frac{d}{dx} \sin{x}))\]

: \(\frac{d}{dx} {x}^{n}=n{x}^{n-1}\)

\[8(\sin{x}+x(\frac{d}{dx} \sin{x}))\]

The derivative of \(\sin{x}\) is \(\cos{x}\)

\[8(\sin{x}+x\cos{x})\]

Done