Problem of the Week

Updated at Sep 19, 2016 8:54 AM

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

How can we find the derivative of x7sin⁡x{x}^{7}\sin{x}?

Check out the solution below!



ddxx7sin⁡x\frac{d}{dx} {x}^{7}\sin{x}

1
Use Product Rule to find the derivative of x7sin⁡x{x}^{7}\sin{x}. The product rule states that (fg)′=f′g+fg′(fg)'=f'g+fg'.
(ddxx7)sin⁡x+x7(ddxsin⁡x)(\frac{d}{dx} {x}^{7})\sin{x}+{x}^{7}(\frac{d}{dx} \sin{x})

2
Use Power Rule: ddxxn=nxn−1\frac{d}{dx} {x}^{n}=n{x}^{n-1}.
7x6sin⁡x+x7(ddxsin⁡x)7{x}^{6}\sin{x}+{x}^{7}(\frac{d}{dx} \sin{x})

3
Use Trigonometric Differentiation: the derivative of sin⁡x\sin{x} is cos⁡x\cos{x}.
7x6sin⁡x+x7cos⁡x7{x}^{6}\sin{x}+{x}^{7}\cos{x}

Done
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