Problem of the Week

Updated at Aug 5, 2024 1:06 PM

For this week we've brought you this calculus problem.

How can we find the derivative of sec⁡y+tan⁡y\sec{y}+\tan{y}?

Here are the steps:



ddysec⁡y+tan⁡y\frac{d}{dy} \sec{y}+\tan{y}

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)).
(ddysec⁡y)+(ddytan⁡y)(\frac{d}{dy} \sec{y})+(\frac{d}{dy} \tan{y})

2
Use Trigonometric Differentiation: the derivative of sec⁡x\sec{x} is sec⁡xtan⁡x\sec{x}\tan{x}.
sec⁡ytan⁡y+(ddytan⁡y)\sec{y}\tan{y}+(\frac{d}{dy} \tan{y})

3
Use Trigonometric Differentiation: the derivative of tan⁡x\tan{x} is sec⁡2x\sec^{2}x.
sec⁡ytan⁡y+sec⁡2y\sec{y}\tan{y}+\sec^{2}y

Done
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