Problem of the Week

Updated at Aug 31, 2026 1:39 PM

To get more practice in calculus, we brought you this problem of the week:

How can we find the derivative of \(\ln{w}+{w}^{8}\)?

Check out the solution below!



\[\frac{d}{dw} \ln{w}+{w}^{8}\]

1
Use Sum Rule: \(\frac{d}{dx} f(x)+g(x)=(\frac{d}{dx} f(x))+(\frac{d}{dx} g(x))\).
\[(\frac{d}{dw} \ln{w})+(\frac{d}{dw} {w}^{8})\]

2
The derivative of \(\ln{x}\) is \(\frac{1}{x}\).
\[\frac{1}{w}+(\frac{d}{dw} {w}^{8})\]

3
Use Power Rule: \(\frac{d}{dx} {x}^{n}=n{x}^{n-1}\).
\[\frac{1}{w}+8{w}^{7}\]

Done
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