Problem of the Week

Updated at Jan 11, 2021 10:20 AM

This week's problem comes from the calculus category.

How can we solve for the derivative of \(\tan{q}+5q\)?

Let's begin!



\[\frac{d}{dq} \tan{q}+5q\]

1
Use Sum Rule: \(\frac{d}{dx} f(x)+g(x)=(\frac{d}{dx} f(x))+(\frac{d}{dx} g(x))\).
\[(\frac{d}{dq} \tan{q})+(\frac{d}{dq} 5q)\]

2
Use Trigonometric Differentiation: the derivative of \(\tan{x}\) is \(\sec^{2}x\).
\[\sec^{2}q+(\frac{d}{dq} 5q)\]

3
Use Power Rule: \(\frac{d}{dx} {x}^{n}=n{x}^{n-1}\).
\[\sec^{2}q+5\]

Done
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