What is the derivative of ln(3x)ln(3x)?

1 Answer
Oct 2, 2016

ln(3x)=yln(3x)=y

e^y=3xey=3x

Now use implicit differentiation. Remember that:

dy/dy*dy/dx=dy/dxdydydydx=dydx

If you use implicit differentiation...

e^y=3xey=3x

Should transform into...

e^y*dy/dx=3eydydx=3

Therefore:

dy/dx=3/e^ydydx=3ey

dy/dx=3/(3x)dydx=33x

dy/dx=1/xdydx=1x


You could also differentiate it like this...

y=ln(3x)y=ln(3x)

y=ln(3)+ln(x)y=ln(3)+ln(x)

*Because of logarithmic rules.

:. dy/dx=1/x