Chapter 11.3, Problem 50E

(a)

To determine

To calculate: The value of $y^{\prime }$ if $x^3-y^3=8$.

(b)

To determine

To prove: The $y^{″}=\frac{2x\left(y-x{y}^{\prime }\right)}{y^3}$ if the value of $y^{\prime }$ is $\frac{x^2}{y^2}$.

(c)

To determine

To prove: The equation $y^{″}=\frac{2x\left(y^3-x^3\right)}{y^5}$ if $y^{\prime }=\frac{x^2}{y^2}$.

(d)

To determine

The validity of statement “$y^{″}=\frac{-16x}{y^5}$” for $x^3-y^3=8$.