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 \(\sec{y}+\tan{y}\)?

Here are the steps:



\[\frac{d}{dy} \sec{y}+\tan{y}\]

1
Use Sum Rule: \(\frac{d}{dx} f(x)+g(x)=(\frac{d}{dx} f(x))+(\frac{d}{dx} g(x))\).
\[(\frac{d}{dy} \sec{y})+(\frac{d}{dy} \tan{y})\]

2
Use Trigonometric Differentiation: the derivative of \(\sec{x}\) is \(\sec{x}\tan{x}\).
\[\sec{y}\tan{y}+(\frac{d}{dy} \tan{y})\]

3
Use Trigonometric Differentiation: the derivative of \(\tan{x}\) is \(\sec^{2}x\).
\[\sec{y}\tan{y}+\sec^{2}y\]

Done
Cymath foriOSAndroid