Problem of the Week

Updated at Sep 14, 2020 3:16 PM

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Sep 14, 2020

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

How would you differentiate \({w}^{3}+\sec{w}\)?

Here are the steps:

\[\frac{d}{dw} {w}^{3}+\sec{w}\]

Use Sum Rule: \(\frac{d}{dx} f(x)+g(x)=(\frac{d}{dx} f(x))+(\frac{d}{dx} g(x))\).

\[(\frac{d}{dw} {w}^{3})+(\frac{d}{dw} \sec{w})\]

Use Power Rule: \(\frac{d}{dx} {x}^{n}=n{x}^{n-1}\).

\[3{w}^{2}+(\frac{d}{dw} \sec{w})\]

Use Trigonometric Differentiation: the derivative of \(\sec{x}\) is \(\sec{x}\tan{x}\).

\[3{w}^{2}+\sec{w}\tan{w}\]

Done