How do you find the derivative of y=ln(5x)y=ln(5x)?

3 Answers
Jul 29, 2014

y'=1/x

Explanation

Suppose, y=ln(b(x))

then using Chain Rule,

y'=1/(b(x))*(b(x))'

Similarly following for the above function yields,

y'=1/(5x)*(5x)'

y'=1/(5x)*5

y'=1/x

Mar 14, 2015

A student comfortable with the natural logarithm function and its properties might think of this:

One could reason as follows:
y=ln(5x)=ln(5)+ln(x).

But ln(5) is a constant, so its derivative is 0.

Therefore, (dy)/(dx) = d/(dx)(ln5+lnx)=d/(dx)(lnx)=1/x.

Mar 24, 2015

Using the Chain Rule you'll get:

y'=1/(5x)*5=1/x

(Derive ln as it is and then multiply by the derivative of the argument, 5x).