Differentiation Question 412
Question: If $ x^{3}+y^{3}-3axy=0 $ , then $ \frac{dy}{dx} $ equals
[RPET 1996]
Options:
A) $ \frac{ay-x^{2}}{y^{2}-ax} $
B) $ \frac{ay-x^{2}}{ay-y^{2}} $
C) $ \frac{x^{2}+ay}{y^{2}+ax} $
D) $ \frac{x^{2}+ay}{ax-y^{2}} $
Show Answer
Answer:
Correct Answer: A
Solution:
$ x^{3}+y^{3}-3axy=0 $
Differentiate w.r.t. x, $ 3x^{2}+3y^{2}.\frac{dy}{dx}-3a( x\frac{dy}{dx}+y )=0 $
$ 3(x^{2}-ay)+3\frac{dy}{dx}(y^{2}-ax)=0 $
$ \Rightarrow $ $ \frac{dy}{dx}=\frac{ay-x^{2}}{y^{2}-ax} $ .
BETA
