What are the derivatives of logarithmic functions?

1 Answer
Oct 21, 2014

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

For example, #d/dx log x= 1/x#

Consider another example.

#d/dx log (1+ x^3)= 1/ (1+x^3) 3x^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. , #1/x *1#

In the second example, the function was #1+x^3#. It's derivative is #3x^2#. Hence derivative of the log function was # 1/ (1+x^3) 3x^2#.