Problem of the Week

Updated at Feb 13, 2017 2:37 PM

How would you differentiate \({x}^{7}-\cot{x}\)?

Below is the solution.



\[\frac{d}{dx} {x}^{7}-\cot{x}\]

1
Use Sum Rule: \(\frac{d}{dx} f(x)+g(x)=(\frac{d}{dx} f(x))+(\frac{d}{dx} g(x))\).
\[(\frac{d}{dx} {x}^{7})-(\frac{d}{dx} \cot{x})\]

2
Use Power Rule: \(\frac{d}{dx} {x}^{n}=n{x}^{n-1}\).
\[7{x}^{6}-(\frac{d}{dx} \cot{x})\]

3
Use Trigonometric Differentiation: the derivative of \(\cot{x}\) is \(-\csc^{2}x\).
\[7{x}^{6}+\csc^{2}x\]

Done
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