Question

How do you differentiate `y = Ln(5x)`?

Answer 1

`(dy)/(dx)=1/x`

Explanation:

Taking this derivative requires knowing the chain rule and the fact that the derivative of `ln(u)=1/u`.

Let `u=5x`. This means that `(du)/(dx)=5`. Then it follows that

`(dy)/(dx)=d/(dx)ln(u)=1/u*(du)/(dx)=1/(5x)*5=1/x`

You can easily prove that for all `a in RR, d/(dx)ln|ax|=1/x`