Problem of the Week

Updated at Dec 1, 2014 5:25 PM

This week's problem comes from the calculus category.

How would you differentiate \(\cos{x}-\sin{x}\)?

Let's begin!



\[\frac{d}{dx} \cos{x}-\sin{x}\]

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

2
Use Trigonometric Differentiation: the derivative of \(\cos{x}\) is \(-\sin{x}\).
\[-\sin{x}-(\frac{d}{dx} \sin{x})\]

3
Use Trigonometric Differentiation: the derivative of \(\sin{x}\) is \(\cos{x}\).
\[-\sin{x}-\cos{x}\]

Done
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