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Implicit Differentiation

If xexy-y=s...

Question

If $x e^{x y} - y = sin x$ then $\frac{d y}{d x}$ at $x = 0$ is

A

0

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B

1

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C

- 1

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D

None of these

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Solution

The correct option is A $0$
Putting $x = 0$ we get, $y = 0$
Now, $x e^{x y} - y = sin x$
Differentiating w.r.t $x$
$e^{x y} + x . e^{x y} {y + x . \frac{d y}{d x}} - \frac{d y}{d x} = cos x$
at $x = 0, y = 0$
$e^{0} + 0. e^{0} (0 + 0) - \frac{d y}{d x} = cos 0$
$\Rightarrow - \frac{d y}{d x} = 0$

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