Problem of the Week

Updated at Sep 22, 2025 8:18 AM

This week we have another calculus problem:

How can we find the derivative of \({m}^{2}+\cos{m}\)?

Let's start!



\[\frac{d}{dm} {m}^{2}+\cos{m}\]

1
Use Sum Rule: \(\frac{d}{dx} f(x)+g(x)=(\frac{d}{dx} f(x))+(\frac{d}{dx} g(x))\).
\[(\frac{d}{dm} {m}^{2})+(\frac{d}{dm} \cos{m})\]

2
Use Power Rule: \(\frac{d}{dx} {x}^{n}=n{x}^{n-1}\).
\[2m+(\frac{d}{dm} \cos{m})\]

3
Use Trigonometric Differentiation: the derivative of \(\cos{x}\) is \(-\sin{x}\).
\[2m-\sin{m}\]

Done
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