Problem of the Week

Updated at May 14, 2018 10:28 AM

This week we have another calculus problem:

How would you differentiate \(\sec{x}+{x}^{8}\)?

Let's start!



\[\frac{d}{dx} \sec{x}+{x}^{8}\]

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

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

3
Use Power Rule: \(\frac{d}{dx} {x}^{n}=n{x}^{n-1}\).
\[\sec{x}\tan{x}+8{x}^{7}\]

Done
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