Problem of the Week

Updated at Dec 11, 2017 11:28 AM

This week we have another calculus problem:

How would you differentiate sec⁡x+csc⁡x\sec{x}+\csc{x}?

Let's start!



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

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

3
Use Trigonometric Differentiation: the derivative of csc⁡x\csc{x} is −csc⁡xcot⁡x-\csc{x}\cot{x}.
sec⁡xtan⁡x−csc⁡xcot⁡x\sec{x}\tan{x}-\csc{x}\cot{x}

Done
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