What's the derivative of 10^(3x-5)?

Answer 1

10^(3x-5) . 3 ln 10

To see this, write 10^(3x-5) = e^((ln 10) (3x-5))
so the derivative is e^((ln 10) (3x-5)) . (ln 10) d/dx (3x-5)
= 10^(3x-5) . (3 ln 10)

It's useful to remember d/dx a^x = a^x (ln a).

Answer 2

Let
10^(3x-5)=A
(3x-5) ln 10 = lnA
3 ln10=A'/A

A'=3 ln10 {10^(3x-5)}