A) \[-\frac{3{{x}^{2}}+8y}{8x+3{{y}^{2}}}\]
B) \[\frac{3{{x}^{2}}+8y}{8x+3{{y}^{2}}}\]
C) \[\frac{3x+8{{y}^{2}}}{8{{x}^{2}}+3y}\]
D) None of these
Correct Answer: A
Solution :
\[{{x}^{3}}+8xy+{{y}^{3}}=64\]\[\Rightarrow 3{{x}^{2}}+8\left( y+x\frac{dy}{dx} \right)+3{{y}^{2}}\frac{dy}{dx}=0\] \[\therefore \frac{dy}{dx}=-\frac{3{{x}^{2}}+8y}{8x+3{{y}^{2}}}\].
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