Q.34. If log (x+y) = 2xy then \frac{dy}{dx} at x=0 is
A. 1
B. -1
C. 2
D. -2
Answer :- A. 1
Explanation :- log (x+y) = 2xy —–(i)
Differentiating w.r.t x, we get
\frac{1}{x+y}\left ( 1+\frac{dy}{dx} \right )=2y+2x\frac{dy}{dx}\frac{1}{x+y}+ \frac{1}{x+y} \frac{dy}{dx}=2y+2x\frac{dy}{dx} –(ii)
At x=0 , Fron (i), we get y=1
From (ii) we get \frac{dy}{dx}|_{x=0}=1