Problem of the Week

Updated at Apr 8, 2019 10:28 AM

This week we have another calculus problem:

How would you differentiate 5p+cos⁡p5p+\cos{p}?

Let's start!



ddp5p+cos⁡p\frac{d}{dp} 5p+\cos{p}

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)).
(ddp5p)+(ddpcos⁡p)(\frac{d}{dp} 5p)+(\frac{d}{dp} \cos{p})

2
Use Power Rule: ddxxn=nxn−1\frac{d}{dx} {x}^{n}=n{x}^{n-1}.
5+(ddpcos⁡p)5+(\frac{d}{dp} \cos{p})

3
Use Trigonometric Differentiation: the derivative of cos⁡x\cos{x} is −sin⁡x-\sin{x}.
5−sin⁡p5-\sin{p}

Done
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