Problem of the Week

Updated at Sep 2, 2019 4:02 PM

How can we solve for the derivative of \(\cot{w}+{w}^{6}\)?

Below is the solution.



\[\frac{d}{dw} \cot{w}+{w}^{6}\]

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

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

3
Use Power Rule: \(\frac{d}{dx} {x}^{n}=n{x}^{n-1}\).
\[6{w}^{5}-\csc^{2}w\]

Done
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