Problem of the Week

Updated at Aug 11, 2014 2:48 PM

This week we have another calculus problem:

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

Let's start!



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

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

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

3
The derivative of \(\ln{x}\) is \(\frac{1}{x}\).
\[\cos{x}+\frac{1}{x}\]

Done
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