# What are the derivatives of logarithmic functions?

Oct 21, 2014

The derivative of a logarithmic function is (1/the function)*derivative of the function.

For example, $\frac{d}{\mathrm{dx}} \log x = \frac{1}{x}$

Consider another example.

$\frac{d}{\mathrm{dx}} \log \left(1 + {x}^{3}\right) = \frac{1}{1 + {x}^{3}} 3 {x}^{2}$

In the first example, the function was x. Thus, derivative of the log function was 1/the function *derivative of the function, i.e. , $\frac{1}{x} \cdot 1$

In the second example, the function was $1 + {x}^{3}$. It's derivative is $3 {x}^{2}$. Hence derivative of the log function was $\frac{1}{1 + {x}^{3}} 3 {x}^{2}$.