what value of x is the derivative of x^3 is equal to the derivative of x^2 + x?

can someone help me out please

not quite sure what you're after, but

d/dx (x^3) = 3x^2
d/dx (x^2+x) = 2x+1

If you want x where they are equal, then

3x^2 = 2x+1
3x^2-2x-1 = 0
(3x+1)(x-1) = 0
x = -1/3 or 1