Problem of the Week

Updated at Apr 13, 2020 4:38 PM

This week we have another calculus problem:

How can we solve for the derivative of 6q+sec⁡q6q+\sec{q}?

Let's start!



ddq6q+sec⁡q\frac{d}{dq} 6q+\sec{q}

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)).
(ddq6q)+(ddqsec⁡q)(\frac{d}{dq} 6q)+(\frac{d}{dq} \sec{q})

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

3
Use Trigonometric Differentiation: the derivative of sec⁡x\sec{x} is sec⁡xtan⁡x\sec{x}\tan{x}.
6+sec⁡qtan⁡q6+\sec{q}\tan{q}

Done
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