Differentiation Question 49
Question: If $ {x^{2/3}}+{y^{2/3}}={a^{2/3}} $ , then $ \frac{dy}{dx}= $
Options:
A) $ {{( \frac{y}{x} )}^{1/3}} $
B) $ -{{( \frac{y}{x} )}^{1/3}} $
C) $ {{( \frac{x}{y} )}^{1/3}} $
D) $ -{{( \frac{x}{y} )}^{1/3}} $
Show Answer
Answer:
Correct Answer: B
Solution:
$ {x^{2/3}}+{y^{2/3}}={a^{2/3}} $
Therefore $ \frac{2}{3}{x^{-1/3}}+\frac{2}{3}{y^{-1/3}}\frac{dy}{dx}=0 $ or $ \frac{dy}{dx}=-{{( \frac{x}{y} )}^{-1/3}}=-{{( \frac{y}{x} )}^{1/3}} $ .
BETA
