# Derivative of lnx Proof

The proof for the derivative of natural log is relatively straightforward using implicit differentiation and chain rule.

## Derivative proof of lnx

Let

By the rule of logarithms, then

Take the derivative with respect to x (treat y as a function of x)

Substitute **x** back in for **e ^{y}**

Divide by **x** and substitute **lnx** back in for y

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