Problem of the Week

Updated at Oct 30, 2017 9:48 AM

This week we have another calculus problem:

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

Let's start!



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

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

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

3
Use Trigonometric Differentiation: the derivative of \(\sin{x}\) is \(\cos{x}\).
\[1+\cos{x}\]

Done
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