how do we know the derivative of ln(x) is 1/x (the definition & implicit differentiation)

証明：ln(x) の導関数は 1/x です | 上級微分 | AP 微積分 AB | カーンアカデミー

Why is the derivative of lnx equal to 1/x?

Why Is the Derivative of ln(x) Equal to 1/x? | Calculus Proof Explained

Derivative of Logarithmic Functions

Proof: Derivative of ln(x) = 1/x by First Principles

ln(x)の微分を求める

How to Differentiate ln x?

Derivative of ln(1/x), calculus 1 tutorial

The Derivative of ln x

Calculus - Finding the derivative with ln(x)

Why is the Derivative of ln(x) = 1/x? | Differentiation

Derivative of ln(x+1) #shorts #calculus

Take the derivative of the natural log function

derivative of ln(1+1/x), two ways

Why is the derivative of lnx = 1/x?

Derivative of ln x

Derivative of ln(1-x)

微分の定義を用いたln(x)の微分

Visual proof: derivative of ln(x) (derivative of natural log of x)