Question

Fill in the blank.

If y = y = [log (x)]²  then `("d"^2"y")/"dx"^2 =` _____.

Answer 1

If y = y = [log (x)]²  then `("d"^2"y")/"dx"^2 =(2(1 − log x))/x^2 `.

Explanation:

y = (log x)²

On differentiating w.r.t. x, we get,

`dy/dx = 2 log x d/dx (log x)`

`dy/dx = 2 log x. 1/x`

`dy/dx = (2log x)/x`

Again differentiating w.r to x, we get,

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

`(d^2y)/(dx^2) = 2 ((x d/dx (log x) − log x d/dx x)/x^2)`

`(d^2y)/(dx^2) = 2 ((x × 1/x − log x × 1)/x^2)`

`(d^2y)/(dx^2) = (2(1 − log x))/x^2`