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\cos{x}-\sin{x}?

Let's begin!



ddxcos⁡x−sin⁡x\frac{d}{dx} \cos{x}-\sin{x}

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)).
(ddxcos⁡x)−(ddxsin⁡x)(\frac{d}{dx} \cos{x})-(\frac{d}{dx} \sin{x})

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

3
Use Trigonometric Differentiation: the derivative of sin⁡x\sin{x} is cos⁡x\cos{x}.
−sin⁡x−cos⁡x-\sin{x}-\cos{x}

Done
Cymath foriOSAndroid