Question

What is the derivative of `ln(4x)`?

Answer 1

1/x

Explanation:

`y = ln4x`

We have a choice. We can either use the chain rule in the form:
`d/dx(ln(u)) = 1/u * (du)/dx` OR we can use properties of logarithms to rewrite the function.

Chain Rule Solution

`d/dx(ln4x) = 1/(4x) * d/dx(4x) = 1/(4x) * 4 = 1/x`

Rewrite Solution

Use `lnab = lna + lnb`, to get:

`d/dx(ln4x) = d/dx(ln4+lnx) = d/dx(ln4) + d/dx(lnx) = 0+(1/x) = 1/x`

(Note that `ln4` is some constant, hence its derivative is `0`.)