Question

How do you find the second derivative of `y=1/x`?

Answer 1

`(d^2y)/(dx^2)=2/x^3`

Explanation:

differentiate using the `color(blue)"power rule"`

`color(orange)"Reminder " color(red)(bar(ul(|color(white)(2/2)color(black)(d/dx(ax^n)=nax^(n-1))color(white)(2/2)|)))`

`y=1/x=x^-1`

`rArrdy/dx=-x^-2`

To obtain the second derivative, differentiate `dy/dx`

`rArr(d^2y)/(dx^2)=2x^-3=2/x^3`