Question

Can you help me with this derivative?
f(x)=ln(3x)

Answer 1

using u-substitution,

u = 3x
du = 3dx

f(x) = ln(u)
f'(x) = u'/u
f'(x) = 3dx/3x
f'(x) = dx/x

Answer 2

You should be in a Math forum but here's the answer anyway.

If you're using the u substitution, you should remember the chain rule, so

u = 3x
u' = 3

f'(x) = d/du[ln(u)] * u'
f'(x) = (1/3x)*3
f'(x) = 1/x

Another solution:
f(x) = ln(3x)
By applying logarithm rules, we get
f(x) = ln(3) + ln(x)

f'(x) = d/dx [ln(3)] + d/dx [ln(x)]
f'(x) = 0 + 1/x

f'(x) = 1/x