How do you differentiate y=12lnx?

1 Answer
Apr 10, 2018

The derivative of 12lnx is 12/x.

Explanation:

Using the fact that the derivative of lnx is 1/x:

color(white)=d/dx[12lnx]

=12*d/dx[lnx]

=12*1/x

=12/x

Here's a short proof for the derivative of lnx.

We know that d/dx[x]=1, that d/dx[e^x]=e^x, also that e^lnx=x:

d/dx[x]=1

d/dx[e^lnx]=1

Chain rule:

e^lnx*d/dx[lnx]=1

x*d/dx[lnx]=1

d/dx[lnx]=1/x