Problem of the Week

Updated at Dec 19, 2016 3:21 PM

For this week we've brought you this calculus problem.

How can we find the derivative of \(\csc{x}-{x}^{3}\)?

Here are the steps:



\[\frac{d}{dx} \csc{x}-{x}^{3}\]

1
Use Sum Rule: \(\frac{d}{dx} f(x)+g(x)=(\frac{d}{dx} f(x))+(\frac{d}{dx} g(x))\).
\[(\frac{d}{dx} \csc{x})+(\frac{d}{dx} -{x}^{3})\]

2
Use Trigonometric Differentiation: the derivative of \(\csc{x}\) is \(-\csc{x}\cot{x}\).
\[-\csc{x}\cot{x}+(\frac{d}{dx} -{x}^{3})\]

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

Done
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