Problem of the Week

Updated at Jul 7, 2014 11:49 AM

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

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

Check out the solution below!



ddxex−tan⁡x\frac{d}{dx} {e}^{x}-\tan{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)).
(ddxex)−(ddxtan⁡x)(\frac{d}{dx} {e}^{x})-(\frac{d}{dx} \tan{x})

2
The derivative of ex{e}^{x} is ex{e}^{x}.
ex−(ddxtan⁡x){e}^{x}-(\frac{d}{dx} \tan{x})

3
Use Trigonometric Differentiation: the derivative of tan⁡x\tan{x} is sec⁡2x\sec^{2}x.
ex−sec⁡2x{e}^{x}-\sec^{2}x

Done
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