Problem of the Week

Updated at Nov 3, 2014 12:49 PM

To get more practice in calculus, we brought you this problem of the week:

How would you differentiate cos⁡x−ex\cos{x}-{e}^{x}?

Check out the solution below!



ddxcos⁡x−ex\frac{d}{dx} \cos{x}-{e}^{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)−(ddxex)(\frac{d}{dx} \cos{x})-(\frac{d}{dx} {e}^{x})

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

3
The derivative of ex{e}^{x} is ex{e}^{x}.
−sin⁡x−ex-\sin{x}-{e}^{x}

Done
Cymath foriOSAndroid