Question

If y is a function of x and $\log (x + y) = 2xy$, then the value of y ' (0) is

• A. 1
• B. -1
• C. 2
• D. 0

Answer 1

The Correct Option is A

Given that, $\log (x + y) = 2 xy$
$\therefore$ At x = 0, $\Rightarrow \log \, (y) = 0 \Rightarrow y = 1$
$\therefore$ To find $\frac{dy}{dx}$ at (0, 1)
On differentiating E (i) w.r.t. x, we get
$\frac{1}{ x + y } \bigg(1 + \frac{dy}{dx}\bigg) = 2x \frac{dy}{dx} + 2y . 1$
$\Rightarrow \frac{dy}{dx} = \frac{ 2 y \, (x + y) - 1}{ 1 - 2 \, (x + y) \, x}$.
$\Rightarrow \left(\frac{dy}{dx}\right)_{(0, 1)} = 1$