Question

How do you differentiate `y= (sqrt(x)+x) / x^2`?

Answer 1

`-(3/(2x^(5/2)) +1/x^2)`

Explanation:

divide terms on numerator by `x^2`

`rArry=x^(1/2)/x^2+x/x^2=x^(-3/2)+x^-1`

now differentiate each term using the `color(blue)" power rule "`

`dy/dx=-3/2 x^(-5/2)-1x^-2`

and writing with positive indices gives.

`dy/dx=-(3/(2x^(5/2))+1/x^2)`