How do you differentiate ln(3x)?

2 Answers
Jul 10, 2016

1/x

Explanation:

chain rule

d/(du) ln u = 1/u

u = 3x, (du)/dx = 3

d/(dx) ln 3x = 1/(3x) * 3 = 1/x

Jul 10, 2016

Let y=ln(3x).

Since d/(dx)[ln(u)] = (u')/(u), let u = 3x, so

y'=3/(3x)=1/x

In fact, we can generalize this formula even more if we notice that for any number a, and y=ln(ax), then y'=a/(ax)=1/x