Question

I'd like to differentiate log 10^(sq root t). Thanks

Answer 1

\[\Large\rm y=\log \sqrt t\]We need to find a derivative?
Do you recall your derivative for natural log?

Answer 2

We can apply a change of base,\[\Large\rm \log_{a}(b)=\frac{\ln(b)}{\ln(a)}\]and then apply what we know with the natural log derivative.

Answer 3

\[\Large\rm y=\log_{10} \sqrt t\]
\[\Large\rm y=\frac{\ln \sqrt t}{\ln(10)}\]No need for quotient rule or anything fancy like that.
The denominator is just constant, let's pull it out of the way.\[\Large\rm y=\left(\frac{1}{\ln(10)}\right)\ln \sqrt t\]

Answer 4

Where you at Larry? What are you thinking? :)

Answer 5

No need to change base at all.
Simply the quest can be written as:
0.5logt. Then derivative is:
0.5/(t.ln10)
That's it.

Answer 6

Change of base is better, that's where the 1/(ln10) is coming from anyway.
You skipped a step by memorizing some weird shortcut.