The Derivative of ln(x): Understanding the Logarithmic Differentiation Technique to Find the Derivative of ln(x)

deriv of lnx

To find the derivative of ln(x), we can use the logarithmic differentiation technique

To find the derivative of ln(x), we can use the logarithmic differentiation technique.

Let y = ln(x), where y is a function of x. To find dy/dx (the derivative of y with respect to x), we’ll take the natural logarithm of both sides of the equation:

ln(y) = ln(ln(x))

Now, we can differentiate implicitly with respect to x on both sides:

1/y * dy/dx = 1/x * 1/ln(x)

To solve for dy/dx, we can multiply both sides by y:

dy/dx = y * (1/x * 1/ln(x))

Since y = ln(x), we substitute it back into the equation:

dy/dx = ln(x) * (1/x * 1/ln(x))

Next, we can simplify the expression:

dy/dx = 1/x

Hence, the derivative of ln(x) is equal to 1/x.

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