Problem of the Week

Updated at Jul 25, 2016 3:36 PM

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

How can we find the derivative of \({x}^{6}+\cot{x}\)?

Here are the steps:



\[\frac{d}{dx} {x}^{6}+\cot{x}\]

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

2
Use Power Rule: \(\frac{d}{dx} {x}^{n}=n{x}^{n-1}\).
\[6{x}^{5}+(\frac{d}{dx} \cot{x})\]

3
Use Trigonometric Differentiation: the derivative of \(\cot{x}\) is \(-\csc^{2}x\).
\[6{x}^{5}-\csc^{2}x\]

Done
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