Question

What are the derivatives of logarithmic functions?

Answer 1

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`.