Question

How do you differentiate `y = -(1/x^2) - sqrtx + (1/2)`?

Answer 1

`y'=2/x^3-1/(2*sqrt(x))`

Explanation:

Writing
`y=-x^(-2)-x^(1/2)+1/2`

After the rule
`(x^n)'=nx^(n-1)`

we get

`y'=2x^(-3)-1/2x^(-1/2)`

`y'=2/x^3-1/(2sqrt(x))`

Answer 2

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

Explanation:

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

`•color(white)(x)d/dx(ax^n)=nax^(n-1)`

`y=-x^-2-x^(1/2)+1/2`

`dy/dx=2x^-3-1/2x^(-1/2)+0`

`color(white)(dy/dx)=2/x^3-1/(2sqrtx)`