Question

Let y be a function of x, such that $\log \left(x+y\right)-2xy=0,$ then $y^{\prime }\left(0\right)$ is

• A. $-1$
• B. $1$
• C. $1/2$
• D. $3/2$

Answer 1

The correct option is A $-1$

Given,

$\log (x+y)=2xy$.....(1).

Now differentiating both sides w.r.to $x$ we get,

or, $\frac{1}{x+y}(1+\frac{dy}{dx})=2x\frac{dy}{dx}+2y$

Now putting $x=0$ in both sides we get,

$1+y^{\prime }\left(0\right)=0$ [ From (1) it is clear that $y\left(0\right)=0$]

or, $y^{\prime }\left(0\right)=-1$.