If (dy)/(dx)=2x+2y then (d^2y)/(dx^2)= 2x+2y+2 4x+4y+4 2x+2y 4x+4y+2

To find the second derivative $\frac{d^2y}{dx^2}$, we need to differentiate the given derivative $\frac{dy}{dx} = 2x + 2y$ with respect to $x$.<br /><br />Differentiating $\frac{dy}{dx} = 2x + 2y$ with respect to $x$, we get:<br /><br />$\frac{d^2y}{dx^2} = \frac{d}{dx}(2x + 2y) = 2 + 2\frac{dy}{dx}$<br /><br />Substituting the given derivative $\frac{dy}{dx} = 2x + 2y$ into the equation, we get:<br /><br />$\frac{d^2y}{dx^2} = 2 + 2(2x + 2y) = 2 + 4x + 4y = 4x + 4y + 2$<br /><br />Therefore, the correct answer is $4x + 4y + 2$.