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

1 Answer
May 31, 2016

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

Explanation:

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

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

(dy)/(dx)=d/(dx)ln(u)=1/u*(du)/(dx)=1/(5x)*5=1/xdydx=ddxln(u)=1ududx=15x5=1x

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