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If $y=e^{\sin \left(\operatorname{cosec}^{-1} x\right)}$ , then $\frac{d y}{d x}=$
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The correct answer is:
$-\frac{e^{\frac{1}{x}}}{x^{2}}$
Given $y=e^{\sin \left(\operatorname{cosec}^{-1} x\right)}$
$\quad=e^{\sin \left(\sin ^{-1} \frac{1}{x}\right)} \Rightarrow y=e^{\frac{1}{x}}$
$\frac{d y}{d x}=e^{\frac{1}{x}}\left(-\frac{1}{x^{2}}\right)$
$\quad=e^{\sin \left(\sin ^{-1} \frac{1}{x}\right)} \Rightarrow y=e^{\frac{1}{x}}$
$\frac{d y}{d x}=e^{\frac{1}{x}}\left(-\frac{1}{x^{2}}\right)$
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