Problem of the Week

Updated at Nov 24, 2025 3:57 PM

How can we find the derivative of \(\sec{t}+2t\)?

Below is the solution.



\[\frac{d}{dt} \sec{t}+2t\]

1
Use Sum Rule: \(\frac{d}{dx} f(x)+g(x)=(\frac{d}{dx} f(x))+(\frac{d}{dx} g(x))\).
\[(\frac{d}{dt} \sec{t})+(\frac{d}{dt} 2t)\]

2
Use Trigonometric Differentiation: the derivative of \(\sec{x}\) is \(\sec{x}\tan{x}\).
\[\sec{t}\tan{t}+(\frac{d}{dt} 2t)\]

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

Done
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