Problem of the Week

Updated at Apr 16, 2018 10:34 AM

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!



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

1
Use Constant Factor Rule: \(\frac{d}{dx} cf(x)=c(\frac{d}{dx} f(x))\)
\[8(\frac{d}{dx} x\sin{x})\]

2
Use Product Rule to find the derivative of \(x\sin{x}\)
The product rule states that \((fg)'=f'g+fg'\)
\[8((\frac{d}{dx} x)\sin{x}+x(\frac{d}{dx} \sin{x}))\]

3
Use Power Rule: \(\frac{d}{dx} {x}^{n}=n{x}^{n-1}\)
\[8(\sin{x}+x(\frac{d}{dx} \sin{x}))\]

4
The derivative of \(\sin{x}\) is \(\cos{x}\)
\[8(\sin{x}+x\cos{x})\]

Done