Problem of the Week

Updated at Oct 25, 2021 5:35 PM

This week's problem comes from the calculus category.

How can we solve for the derivative of \(\csc{y}+6y\)?

Let's begin!



\[\frac{d}{dy} \csc{y}+6y\]

1
Use Sum Rule: \(\frac{d}{dx} f(x)+g(x)=(\frac{d}{dx} f(x))+(\frac{d}{dx} g(x))\).
\[(\frac{d}{dy} \csc{y})+(\frac{d}{dy} 6y)\]

2
Use Trigonometric Differentiation: the derivative of \(\csc{x}\) is \(-\csc{x}\cot{x}\).
\[-\csc{y}\cot{y}+(\frac{d}{dy} 6y)\]

3
Use Power Rule: \(\frac{d}{dx} {x}^{n}=n{x}^{n-1}\).
\[-\csc{y}\cot{y}+6\]

Done
Cymath foriOSAndroid