Question

If $xe^{xy} = y + \sin^{2}x$, then at $x = 0$, $\frac{dy}{dx}$=

• A. – 1
• B. – 2
• C. 1
• D. 2

Answer 1

Answer: (C)

1

Answer 2

We are given that $xe^{xy} = y + \sin^{2}x$

When $x = 0$, we get $y = 0$

Differentiating both sides w.r.t. x, we get,

$e^{xy} + xe^{xy}\left\lbrack x\frac{dy}{dx} + y \right\rbrack = \frac{dy}{dx} + 2\sin x\cos x$

Putting, $x = 0$, $y = 0$, we get $\frac{dy}{dx} = 1$.