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Question: Answered & Verified by Expert
If $y=e^{\sin \left(\operatorname{cosec}^{-1} x\right)}$ , then $\frac{d y}{d x}=$
MathematicsDifferentiationMHT CETMHT CET 2020 (14 Oct Shift 2)
Options:
  • A $\frac{e^{\frac{1}{x}}}{x^{2}}$
  • B $-\frac{e^{\frac{1}{x}}}{x^{2}}$
  • C 0
  • D $e^{\cos \left(\operatorname{cosec}^{-1} x\right)}$
Solution:
1821 Upvotes Verified Answer
The correct answer is: $-\frac{e^{\frac{1}{x}}}{x^{2}}$
Given $y=e^{\sin \left(\operatorname{cosec}^{-1} x\right)}$
$\quad=e^{\sin \left(\sin ^{-1} \frac{1}{x}\right)} \Rightarrow y=e^{\frac{1}{x}}$
$\frac{d y}{d x}=e^{\frac{1}{x}}\left(-\frac{1}{x^{2}}\right)$

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