Evaluate the derivative of y=x^3/3 - 2sqrtx for x=3

To find the derivative of y = x^3/3 - 2sqrtx  at x =
3.

To find dy/dx at x= 3 , we first find the derivative
.Then find its value at x=3.

Let f(x) = y = x^3/3 -
2sqrtx.

f'(x) = dy/dx = {x^3/3 -
2x^(1/2)}'

dy/dx = (x^3/3)' -
2(x^1/2)'.

We use (cx^n)' =cn*x^(n-1) ,  where c is any
constant but not zero.

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

dy/dx = f'(x) =
x^2-1/x^(1/2)

f'(3) =
3^2-1/3^(1/2)

f'(3) = 9 -(sqrt3)/3.