Problem of the Week

Updated at Jun 24, 2024 5:25 PM

This week's problem comes from the calculus category.

How would you differentiate \(14n+\sin{n}\)?

Let's begin!



\[\frac{d}{dn} 14n+\sin{n}\]

1
Use Sum Rule: \(\frac{d}{dx} f(x)+g(x)=(\frac{d}{dx} f(x))+(\frac{d}{dx} g(x))\).
\[(\frac{d}{dn} 14n)+(\frac{d}{dn} \sin{n})\]

2
Use Power Rule: \(\frac{d}{dx} {x}^{n}=n{x}^{n-1}\).
\[14+(\frac{d}{dn} \sin{n})\]

3
Use Trigonometric Differentiation: the derivative of \(\sin{x}\) is \(\cos{x}\).
\[14+\cos{n}\]

Done
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