Question

How do you find the second derivative of `ln(2x)`?

Answer 1

`-1/x^2`

Explanation:

`color(orange)"Reminder " color(red)(bar(ul(|color(white)(2/2)color(black)(d/dx[ln(f(x))]=(f'(x))/(f(x)))color(white)(2/2)|)))`

`"let " f(x)=ln(2x)`

`rArrf'(x)=1/(2x).d/dx(2x)=2/(2x)=1/x=x^-1`

`" To find the second derivative " f''(x), "differentiate" f'(x)`

`rArrf''(x)=-1x^-2=-1/x^2`