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

Let's begin!



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

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

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

3
Use Power Rule: \(\frac{d}{dx} {x}^{n}=n{x}^{n-1}\).
\[4{m}^{3}-\csc^{2}m\]

Done
Cymath foriOSAndroid