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

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

Derivative of Logarithmic Functions

Derivative of ln(1+x^2) || Differentiation of ln(x^2+1)

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

Take the derivative of the natural log function

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

Derivative of (1/2)ln(x+1) - (1/2)ln(x-1)

Derivative of -ln(x-1) + ln(x-2)

Derivatives of Exponential Functions & Logarithmic Differentiation Calculus lnx, e^2x, x^x, x^sinx

Derivative of ln(x^2 + 1)

微分の定義を用いたln(x)の微分

The Derivative of ln x

Calculus - Finding the derivative with ln(x)

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

Why is the derivative of lnx = 1/x?

derivative of ln(x+sqrt(x^2-1)), calculus 1 tutorial

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

Derivative of (1/2)ln(x-1) - (1/2)ln(x+1)

Learn to Differentiate ln(x²) in 40 seconds