Derivative of ln(x) | Calculation and Explanation of the Natural Logarithm Function’s Rate of Change

d/dx ln(x)

To find the derivative of the natural logarithm function ln(x), we can use the derivative rules for logarithmic functions

To find the derivative of the natural logarithm function ln(x), we can use the derivative rules for logarithmic functions. The derivative of ln(x) with respect to x can be calculated using the chain rule as follows:

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

However, the derivative of x with respect to x is simply 1. Therefore, the derivative of ln(x) is:

d/dx ln(x) = 1/x

So, the derivative of the natural logarithm function ln(x) is 1/x.

In simpler terms, this means that the rate of change of the natural logarithm of x with respect to x is equal to 1 divided by x.

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