y = x^3(x + 1)^2
dy/dx = 3x^2(x + 1)^2 + 2x^3(x + 1)
OR if you have not been taught how to differentiate in this way
y = x^3(x + 1)^2
y = x^3(x + 1)(x + 1) = x^3(x^2 + 2x + 1) = x^5 + 2x^4 + x^3
dy/dx = 5x^4 + 8x^3 + 3x^2
They both give you the same answer (if you times out the brackets in the first answer you can check that for yourself)