Problem of the Week

Updated at Dec 11, 2017 11:28 AM

This week we have another calculus problem:

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

Let's start!



\[\frac{d}{dx} \sec{x}+\csc{x}\]

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

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

3
Use Trigonometric Differentiation: the derivative of \(\csc{x}\) is \(-\csc{x}\cot{x}\).
\[\sec{x}\tan{x}-\csc{x}\cot{x}\]

Done
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