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 \(\sin{m}+{m}^{4}\)?

Let's begin!



\[\frac{d}{dm} \sin{m}+{m}^{4}\]

1
Use Sum Rule: \(\frac{d}{dx} f(x)+g(x)=(\frac{d}{dx} f(x))+(\frac{d}{dx} g(x))\).
\[(\frac{d}{dm} \sin{m})+(\frac{d}{dm} {m}^{4})\]

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

3
Use Power Rule: \(\frac{d}{dx} {x}^{n}=n{x}^{n-1}\).
\[\cos{m}+4{m}^{3}\]

Done
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