Question

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

Answer 1

`ln(3x)=y`

`e^y=3x`

Now use implicit differentiation. Remember that:

`dy/dy*dy/dx=dy/dx`

If you use implicit differentiation...

`e^y=3x`

Should transform into...

`e^y*dy/dx=3`

Therefore:

`dy/dx=3/e^y`

`dy/dx=3/(3x)`

`dy/dx=1/x`

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You could also differentiate it like this...

`y=ln(3x)`

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

*Because of logarithmic rules.

`:. dy/dx=1/x`