Question

derivative of y

y=ln9x

answer is 1/x but I thought it was 1/9x

d(lnu) = u' / u

so why is u "x" and not "9x"?

Answer 1

Because of the chain rule. After you have 1/(9x) you multiply by d/dx(9x) which is 9.
So 9/9x becomes 1/x

Answer 2

or you can note that \(\ln(9x)=\ln(9)+\ln(x)\) and since \(\ln(9)\) is a constant, the derivative is \(\frac{1}{x}\)

Answer 3

Thanks!