Question

If y is a function of x and $ln(x+y)-2xy=0,$ then the value of y'(0) is equal to

• A. 1
• B. 2
• C. 3
• D. 4

Answer 1

The correct option is A 1

$ln(x+y)-2xy=0$ ...(1)
put $x=0$, we get $ln(0+y)-0=0$
$\Rightarrow y=1$
now, diff. (1)
$\frac{1+y^{\prime }}{x+y}-2y-2x{y}^{\prime }=0$
$y^{\prime }[1-2x(x+y\left)\right]=2y(x+y)-1$
$y^{\prime }=\frac{2y(x+y)-1}{1-2x(x+y)}$
now, $y^{\prime }\left(0\right)=\frac{2-1}{1-0}=1$
Ans: A