Problem of the Week

Updated at Dec 26, 2016 3:52 PM

How would you differentiate \(2x+\sin{x}\)?

Below is the solution.



\[\frac{d}{dx} 2x+\sin{x}\]

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

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

3
Use Trigonometric Differentiation: the derivative of \(\sin{x}\) is \(\cos{x}\).
\[2+\cos{x}\]

Done
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