Problem of the Week

Updated at Nov 30, 2015 4:36 PM

For this week we've brought you this calculus problem.

How can we find the derivative of \(\sin{x}+4x\)?

Here are the steps:



\[\frac{d}{dx} \sin{x}+4x\]

1
Use Sum Rule: \(\frac{d}{dx} f(x)+g(x)=(\frac{d}{dx} f(x))+(\frac{d}{dx} g(x))\).
\[(\frac{d}{dx} \sin{x})+(\frac{d}{dx} 4x)\]

2
Use Trigonometric Differentiation: the derivative of \(\sin{x}\) is \(\cos{x}\).
\[\cos{x}+(\frac{d}{dx} 4x)\]

3
Use Power Rule: \(\frac{d}{dx} {x}^{n}=n{x}^{n-1}\).
\[\cos{x}+4\]

Done
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