Question

find the second derivative in terms of x and y

y^2 = x^3

Answer 1

find 1st derivative
\[2y \frac{dy}{dx} = 3x^{2}\]
\[\frac{dy}{dx} = \frac{3x^{2}}{2y}\]
differentiate again using quotient rule
\[\frac{d^{2}y}{dx} = \frac{(6x)(2y)-(3x^{2})(2dy/dx)}{(2y)^{2}}\]
sub in 1st derivative and simplify