Problem of the Week

Updated at Oct 31, 2022 5:10 PM

This week's problem comes from the calculus category.

How would you differentiate sec⁡z+8z\sec{z}+8z?

Let's begin!



ddzsec⁡z+8z\frac{d}{dz} \sec{z}+8z

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)).
(ddzsec⁡z)+(ddz8z)(\frac{d}{dz} \sec{z})+(\frac{d}{dz} 8z)

2
Use Trigonometric Differentiation: the derivative of sec⁡x\sec{x} is sec⁡xtan⁡x\sec{x}\tan{x}.
sec⁡ztan⁡z+(ddz8z)\sec{z}\tan{z}+(\frac{d}{dz} 8z)

3
Use Power Rule: ddxxn=nxn−1\frac{d}{dx} {x}^{n}=n{x}^{n-1}.
sec⁡ztan⁡z+8\sec{z}\tan{z}+8

Done
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