Derivatives Involving ln x

Recall that if y = ln x, then e^y = x. So if we differentiate both sides of the latter equation implicitly, we will have e^y y´ = 1, so y´ = 1/e^y but e^y = x. Therefore, if y = ln x, then y´ = 1/x. In other words the derivative of ln x = 1/x.