Differentiation Question 21
Question: If $ x^{m}y^{n}=2{{(x+y)}^{m+n}}, $ the value of $ \frac{dy}{dx} $ is
[MP PET 2003]
Options:
A) $ x+y $
B) $ x/y $
C) $ y/x $
D) $ x-y $
Show Answer
Answer:
Correct Answer: C
Solution:
$ x^{m}y^{n}=2{{(x+y)}^{m+n}}\Rightarrow m\log x+n\log y=\log 2+(m+n)\log (x+y) $
Differentiating both sides w.r.t. x, $ \frac{m}{x}+\frac{n}{y}\frac{dy}{dx}=\frac{m+n}{x+y}[ 1+\frac{dy}{dx} ] $
Therefore $ \frac{dy}{dx}=\frac{y}{x} $ .
BETA
