Why is the derivative of #ln -x = 1/x#?

1 Answer
Mar 30, 2015

This is because the chain rule says:

#y=f(g(x))=f'(g(x))*g'(x)#.

So:

#y=ln(-x)rArry'=1/-x*(-1)=1/x#.

The #1/-x# is the derivative of the logarithmic function and the #-1# is the derivative of #-x#.

For the same reason in this integral:

#int1/xdx=ln|x|+c#

we have to put the absolue value to #x#, because we want to write all the primitive functions.