Problem of the Week

Updated at Apr 27, 2020 2:54 PM

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

How can we find the derivative of 6u+sec⁡u6u+\sec{u}?

Check out the solution below!



ddu6u+sec⁡u\frac{d}{du} 6u+\sec{u}

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)).
(ddu6u)+(ddusec⁡u)(\frac{d}{du} 6u)+(\frac{d}{du} \sec{u})

2
Use Power Rule: ddxxn=nxn−1\frac{d}{dx} {x}^{n}=n{x}^{n-1}.
6+(ddusec⁡u)6+(\frac{d}{du} \sec{u})

3
Use Trigonometric Differentiation: the derivative of sec⁡x\sec{x} is sec⁡xtan⁡x\sec{x}\tan{x}.
6+sec⁡utan⁡u6+\sec{u}\tan{u}

Done
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