Problem of the Week

Updated at Sep 5, 2022 12:09 PM

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

How can we find the derivative of \(\csc{v}+9v\)?

Check out the solution below!



\[\frac{d}{dv} \csc{v}+9v\]

1
Use Sum Rule: \(\frac{d}{dx} f(x)+g(x)=(\frac{d}{dx} f(x))+(\frac{d}{dx} g(x))\).
\[(\frac{d}{dv} \csc{v})+(\frac{d}{dv} 9v)\]

2
Use Trigonometric Differentiation: the derivative of \(\csc{x}\) is \(-\csc{x}\cot{x}\).
\[-\csc{v}\cot{v}+(\frac{d}{dv} 9v)\]

3
Use Power Rule: \(\frac{d}{dx} {x}^{n}=n{x}^{n-1}\).
\[-\csc{v}\cot{v}+9\]

Done
Cymath foriOSAndroid