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⁡n14n+\sin{n}?

Let's begin!



ddn14n+sin⁡n\frac{d}{dn} 14n+\sin{n}

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)).
(ddn14n)+(ddnsin⁡n)(\frac{d}{dn} 14n)+(\frac{d}{dn} \sin{n})

2
Use Power Rule: ddxxn=nxn−1\frac{d}{dx} {x}^{n}=n{x}^{n-1}.
14+(ddnsin⁡n)14+(\frac{d}{dn} \sin{n})

3
Use Trigonometric Differentiation: the derivative of sin⁡x\sin{x} is cos⁡x\cos{x}.
14+cos⁡n14+\cos{n}

Done
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