How to Evaluate the Derivative of a Logarithmic Function with a Base of 10?

[banfill_89]

Homework Statement

if g(t)=(10^t)(log...t) then evaluate g'(10)
......10 <---------(my attempt at a log base 10)

Homework Equations

im completely lost...i don't know if i should take the ln of both sides...or what to do really.

The Attempt at a Solution

 

[rocomath]

g(t)=10^t\log t

Naw don't take log of both sides, just differentiate from the get go :)

\frac{d}{dx}a^x=a^x\log a

Don't forget the Product rule.