Differentiation Question 427
Question: If $ \ln (x+y)=2xy, $ then $ y’(0) $ =
[IIT Screening 2004]
Options:
A) 1
B) -1
C) 2
D) 0
Show Answer
Answer:
Correct Answer: A
Solution:
$ \ln (x+y)=2xy $
Differentiate both sides w.r.t x, $ ( \frac{1}{x+y} )( 1+\frac{dy}{dx} )=2( x\frac{dy}{dx}+y ) $
Therefore $ \frac{dy}{dx}=\frac{1-2xy-2y^{2}}{2x^{2}+2xy-1} $
As at $ x=0,y=1 $ , (From $ \ln (x+y)=2xy $ ) Hence $ y’(0)=\frac{1-2}{-1}=1 $ .
BETA
