Problem of the Week

Updated at May 10, 2021 12:01 PM

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

How would you differentiate \(9x+\sec{x}\)?

Here are the steps:



\[\frac{d}{dx} 9x+\sec{x}\]

1
Use Sum Rule: \(\frac{d}{dx} f(x)+g(x)=(\frac{d}{dx} f(x))+(\frac{d}{dx} g(x))\).
\[(\frac{d}{dx} 9x)+(\frac{d}{dx} \sec{x})\]

2
Use Power Rule: \(\frac{d}{dx} {x}^{n}=n{x}^{n-1}\).
\[9+(\frac{d}{dx} \sec{x})\]

3
Use Trigonometric Differentiation: the derivative of \(\sec{x}\) is \(\sec{x}\tan{x}\).
\[9+\sec{x}\tan{x}\]

Done
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