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STD 12 - 5. continuity and differentiation — JEE STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceJEESTD 12 - 5. continuity and differentiation4 Marks
MCQ
If  $xe^{xy}=y+e^{\sin 2x} ,$ then at $x=0, \, \frac{dy}{dx}$ is equal to -
  • ✓
    $-1$
  • B
    $1$
  • C
    $0$
  • D
    $2$
✓

Answer

Correct option: A.
$-1$
a
$e^{x y} \cdot 1+x e^{x y}\left(y+x \frac{d y}{d x}\right)=\frac{d y}{d x}+e^{\sin 2 x} \cdot \cos 2 x$

at $x=0$

$1+0=\left(\frac{\mathrm{dy}}{\mathrm{dx}}\right)_{\mathrm{x}=0}+2 \Rightarrow\left(\frac{\mathrm{dy}}{\mathrm{dx}}\right)_{\mathrm{x}=0}=-1$

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