How to Find the Derivative of the Natural Logarithm Function | Step-by-Step Guide and Chain Rule

d/dx ln(x)

To find the derivative of the natural logarithm function, ln(x), with respect to x, we can use the chain rule

To find the derivative of the natural logarithm function, ln(x), with respect to x, we can use the chain rule. The chain rule is a formula that allows us to find the derivative of a composition of functions.

Step 1: Determine the function inside the natural logarithm. In our case, the function inside the natural logarithm is x.

Step 2: Write the derivative of the natural logarithm function using the chain rule. The derivative of ln(u) with respect to u is 1/u. Since u = x in this case, the derivative of ln(x) will be 1/x.

Therefore, the derivative of ln(x) with respect to x is 1/x.

In summary, d/dx ln(x) = 1/x.

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