Find d2ydx2 if 2x3−2y3=50 . (1 point) Responses 6x2−6y2 6 x 2 − 6 y 2 x2y2 x 2 y 2 6x2y2 6 x 2 y 2 −50xy5 − 50 x y 5 yx
To find d^2y/dx^2, we need to differentiate the given equation twice with respect to x.
First, let's differentiate the given equation with respect to x:
6x^2 - 6y^2(dy/dx) = 0
Next, let's differentiate this equation again with respect to x:
d(6x^2)/dx - d(6y^2(dy/dx))/dx = 0
12x - 12y^2(dy/dx)^2 - 12y(dy^2/dx^2) = 0
Next, let's solve for (dy^2/dx^2):
12y(dy^2/dx^2) = 12x - 12x^2 + 12y^2(dy/dx)^2
dy^2/dx^2 = (12x - 12x^2 + 12y^2(dy/dx)^2) / (12y)
Therefore, the correct answer is (12x - 12x^2 + 12y^2(dy/dx)^2) / (12y).