Problem of the Week

Updated at Aug 15, 2016 1:05 PM

This week's problem comes from the calculus category.

How can we solve for the derivative of ex−sec⁡x{e}^{x}-\sec{x}?

Let's begin!



ddxex−sec⁡x\frac{d}{dx} {e}^{x}-\sec{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)−(ddxsec⁡x)(\frac{d}{dx} {e}^{x})-(\frac{d}{dx} \sec{x})

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

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

Done
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