Differentiation Question 146
Question: If $ x^{3}+8xy+y^{3}=64 $ ,then $ \frac{dy}{dx}= $
[AI CBSE 1979]
Options:
A) $ -\frac{3x^{2}+8y}{8x+3y^{2}} $
B) $ \frac{3x^{2}+8y}{8x+3y^{2}} $
C) $ \frac{3x+8y^{2}}{8x^{2}+3y} $
D) None of these
Show Answer
Answer:
Correct Answer: A
Solution:
$ x^{3}+8xy+y^{3}=64 $
$ \Rightarrow 3x^{2}+8( y+x\frac{dy}{dx} )+3y^{2}\frac{dy}{dx}=0 $
$ \therefore \frac{dy}{dx}=-\frac{3x^{2}+8y}{8x+3y^{2}} $ .
BETA
