Question

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

Answer 1

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.