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 \(\sec{z}+8z\)?

Let's begin!



\[\frac{d}{dz} \sec{z}+8z\]

1
Use Sum Rule: \(\frac{d}{dx} f(x)+g(x)=(\frac{d}{dx} f(x))+(\frac{d}{dx} g(x))\).
\[(\frac{d}{dz} \sec{z})+(\frac{d}{dz} 8z)\]

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

3
Use Power Rule: \(\frac{d}{dx} {x}^{n}=n{x}^{n-1}\).
\[\sec{z}\tan{z}+8\]

Done
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