Problem of the Week

Updated at Aug 17, 2015 5:04 PM

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

How would you differentiate sec⁡x+sin⁡x\sec{x}+\sin{x}?

Check out the solution below!



ddxsec⁡x+sin⁡x\frac{d}{dx} \sec{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)).
(ddxsec⁡x)+(ddxsin⁡x)(\frac{d}{dx} \sec{x})+(\frac{d}{dx} \sin{x})

2
Use Trigonometric Differentiation: the derivative of sec⁡x\sec{x} is sec⁡xtan⁡x\sec{x}\tan{x}.
sec⁡xtan⁡x+(ddxsin⁡x)\sec{x}\tan{x}+(\frac{d}{dx} \sin{x})

3
Use Trigonometric Differentiation: the derivative of sin⁡x\sin{x} is cos⁡x\cos{x}.
sec⁡xtan⁡x+cos⁡x\sec{x}\tan{x}+\cos{x}

Done
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