Problem of the Week

Updated at Jan 13, 2025 12:15 PM

This week's problem comes from the calculus category.

How can we find the derivative of cot⁡m+m4\cot{m}+{m}^{4}?

Let's begin!



ddmcot⁡m+m4\frac{d}{dm} \cot{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)).
(ddmcot⁡m)+(ddmm4)(\frac{d}{dm} \cot{m})+(\frac{d}{dm} {m}^{4})

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

3
Use Power Rule: ddxxn=nxn−1\frac{d}{dx} {x}^{n}=n{x}^{n-1}.
4m3−csc⁡2m4{m}^{3}-\csc^{2}m

Done
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