Derivative of ln(x)

Again, this is another post for my own amusement/memory

The derivative of log_e(x) is \frac{1}{x} – but I could find no proof for that online, so I worked out my own (admittedly this is not a complex problem).

Let y=e^x, then x=log_e(y)

We know \frac{dy}{dx} = e^x so \frac{dx}{dy} = \frac{d}{dy}log_e(y) = \frac{1}{e^x} =\frac{1}{y}

Hence, to restate this in the standard manner \frac{d}{dx}ln(x) = \frac{1}{x}

One response to “Derivative of ln(x)”

  1. […] again we start from the proposition that there exists a number such that and hence (see here for why the second follows from the […]

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