Problem of the Week

Updated at Feb 7, 2022 11:39 AM

To get more practice in calculus, we brought you this problem of the week:

How can we find the derivative of \({w}^{4}+\cot{w}\)?

Check out the solution below!



\[\frac{d}{dw} {w}^{4}+\cot{w}\]

1
Use Sum Rule: \(\frac{d}{dx} f(x)+g(x)=(\frac{d}{dx} f(x))+(\frac{d}{dx} g(x))\).
\[(\frac{d}{dw} {w}^{4})+(\frac{d}{dw} \cot{w})\]

2
Use Power Rule: \(\frac{d}{dx} {x}^{n}=n{x}^{n-1}\).
\[4{w}^{3}+(\frac{d}{dw} \cot{w})\]

3
Use Trigonometric Differentiation: the derivative of \(\cot{x}\) is \(-\csc^{2}x\).
\[4{w}^{3}-\csc^{2}w\]

Done
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