Font (2 3) - + Letter spacing (4 5) - + Word spacing (6 7) - + Line spacing (8 9) - +

3.25 The derivative of $\log$

Example

The derivative of the log function is ${{d}\over{dx}}\log x=1/x$ for $x>0$ .

Solution. From $y=\log x$ , we let $x=e^{y}$ ; then

{{dy}\over{dx}}=1/{{dx}\over{dy}}=1/e^{y}=1/x

for $x>0.$