Problem of the Week

Updated at Feb 16, 2026 12:49 PM

To get more practice in calculus, we brought you this problem of the week:

How would you differentiate \(\cot{v}+5v\)?

Check out the solution below!



\[\frac{d}{dv} \cot{v}+5v\]

1
Use Sum Rule: \(\frac{d}{dx} f(x)+g(x)=(\frac{d}{dx} f(x))+(\frac{d}{dx} g(x))\).
\[(\frac{d}{dv} \cot{v})+(\frac{d}{dv} 5v)\]

2
Use Trigonometric Differentiation: the derivative of \(\cot{x}\) is \(-\csc^{2}x\).
\[-\csc^{2}v+(\frac{d}{dv} 5v)\]

3
Use Power Rule: \(\frac{d}{dx} {x}^{n}=n{x}^{n-1}\).
\[5-\csc^{2}v\]

Done
Cymath foriOSAndroid