Problem of the Week

Updated at Jan 12, 2015 9:25 AM

This week's problem comes from the calculus category.

How would you differentiate \({e}^{x}-\csc{x}\)?

Let's begin!



\[\frac{d}{dx} {e}^{x}-\csc{x}\]

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

2
The derivative of \({e}^{x}\) is \({e}^{x}\).
\[{e}^{x}-(\frac{d}{dx} \csc{x})\]

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

Done
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