Problem of the Week

Updated at Apr 24, 2023 8:20 AM

This week's problem comes from the calculus category.

How can we solve for the derivative of sin⁡m+m4\sin{m}+{m}^{4}?

Let's begin!



ddmsin⁡m+m4\frac{d}{dm} \sin{m}+{m}^{4}

1
Use Sum Rule: ddxf(x)+g(x)=(ddxf(x))+(ddxg(x))\frac{d}{dx} f(x)+g(x)=(\frac{d}{dx} f(x))+(\frac{d}{dx} g(x)).
(ddmsin⁡m)+(ddmm4)(\frac{d}{dm} \sin{m})+(\frac{d}{dm} {m}^{4})

2
Use Trigonometric Differentiation: the derivative of sin⁡x\sin{x} is cos⁡x\cos{x}.
cos⁡m+(ddmm4)\cos{m}+(\frac{d}{dm} {m}^{4})

3
Use Power Rule: ddxxn=nxn−1\frac{d}{dx} {x}^{n}=n{x}^{n-1}.
cos⁡m+4m3\cos{m}+4{m}^{3}

Done
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