Problem of the Week

Updated at Jun 4, 2018 5:28 PM

This week we have another calculus problem:

How would you differentiate sec⁡x+x9\sec{x}+{x}^{9}?

Let's start!



ddxsec⁡x+x9\frac{d}{dx} \sec{x}+{x}^{9}

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)).
(ddxsec⁡x)+(ddxx9)(\frac{d}{dx} \sec{x})+(\frac{d}{dx} {x}^{9})

2
Use Trigonometric Differentiation: the derivative of sec⁡x\sec{x} is sec⁡xtan⁡x\sec{x}\tan{x}.
sec⁡xtan⁡x+(ddxx9)\sec{x}\tan{x}+(\frac{d}{dx} {x}^{9})

3
Use Power Rule: ddxxn=nxn−1\frac{d}{dx} {x}^{n}=n{x}^{n-1}.
sec⁡xtan⁡x+9x8\sec{x}\tan{x}+9{x}^{8}

Done
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