What is the derivative of log x?

The derivative of log x is 1/(x ln 10)​.

To find this derivative, we use the differentiation rules for logarithmic functions. For the natural logarithm function, ln x (or loge​ x), where the base is the constant e, the derivative is:

d/dx​ (ln x) = 1/x​

This result comes from applying the chain rule of differentiation. The natural logarithm function represents the logarithm to the base e, approximately 2.71828.

So, the derivative of the natural logarithm function, log x, with respect to x is 1/x​, derived from the differentiation rules for logarithmic functions, where the derivative is inversely proportional to x.