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

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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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