Problem of the Week

Updated at Apr 13, 2015 9:00 AM

This week's problem comes from the calculus category.

How can we find the derivative of x+sec⁡xx+\sec{x}?

Let's begin!



ddxx+sec⁡x\frac{d}{dx} x+\sec{x}

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)).
(ddxx)+(ddxsec⁡x)(\frac{d}{dx} x)+(\frac{d}{dx} \sec{x})

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

3
Use Trigonometric Differentiation: the derivative of sec⁡x\sec{x} is sec⁡xtan⁡x\sec{x}\tan{x}.
1+sec⁡xtan⁡x1+\sec{x}\tan{x}

Done
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