Problem of the Week

Updated at Sep 14, 2020 3:16 PM

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

How would you differentiate w3+sec⁡w{w}^{3}+\sec{w}?

Here are the steps:



ddww3+sec⁡w\frac{d}{dw} {w}^{3}+\sec{w}

1
Use Sum Rule: ddxf(x)+g(x)=(ddxf(x))+(ddxg(x))\frac{d}{dx} f(x)+g(x)=(\frac{d}{dx} f(x))+(\frac{d}{dx} g(x)).
(ddww3)+(ddwsec⁡w)(\frac{d}{dw} {w}^{3})+(\frac{d}{dw} \sec{w})

2
Use Power Rule: ddxxn=nxn−1\frac{d}{dx} {x}^{n}=n{x}^{n-1}.
3w2+(ddwsec⁡w)3{w}^{2}+(\frac{d}{dw} \sec{w})

3
Use Trigonometric Differentiation: the derivative of sec⁡x\sec{x} is sec⁡xtan⁡x\sec{x}\tan{x}.
3w2+sec⁡wtan⁡w3{w}^{2}+\sec{w}\tan{w}

Done
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