What is the Derivative of Log (x)

Question – What is the derivative of log (x)?

Answer –

In order to understand “log,” we must first define it. Using “log” as a logarithm is widespread. I.e., it’s the base 10 logarithms. The default base for “log” is 10 if no base is specified. This means logarithms can be expressed as logarithms.

Derivation of log (x)

We need to find the logarithmic derivative of x.

Solution

Exponentiation functions are defined as the inverse of log functions:

y = ln(x) = x = e^y

y = log_a(x) = x = a^y

We can use implicit differentiation to derive the derivatives of ln(x) and loga(x) because we know how to differentiate exponentials (x).

d/ dx [ln(x)] = 1/x

d/ dx [log_a(x)] = 1/ x ln a

Answer

The derivative of log x = 1/ x ln a