Problem of the Week

Updated at Jul 8, 2024 4:54 PM

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

How can we find the derivative of 7x+tan⁡x7x+\tan{x}?

Check out the solution below!



ddx7x+tan⁡x\frac{d}{dx} 7x+\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)).
(ddx7x)+(ddxtan⁡x)(\frac{d}{dx} 7x)+(\frac{d}{dx} \tan{x})

2
Use Power Rule: ddxxn=nxn−1\frac{d}{dx} {x}^{n}=n{x}^{n-1}.
7+(ddxtan⁡x)7+(\frac{d}{dx} \tan{x})

3
Use Trigonometric Differentiation: the derivative of tan⁡x\tan{x} is sec⁡2x\sec^{2}x.
7+sec⁡2x7+\sec^{2}x

Done
Cymath foriOSAndroid