AP EAMCET · Maths · Differentiation
If \(y=\operatorname{cosec}^{-1}(x)\) and \(\frac{d y}{d x}=\frac{-1}{|x| \sqrt{x^2-1}}\), then
- A \(y \in\left(-\frac{\pi}{2}, 0\right)\)
- B \(y \in\left(-\frac{\pi}{2}, 2 \pi\right)\)
- C \(y \in\left(-\frac{\pi}{2}, 0\right) \cup\left(0, \frac{\pi}{2}\right)\)
- D \(y \in R\)
Answer & Solution
Correct Answer
(C) \(y \in\left(-\frac{\pi}{2}, 0\right) \cup\left(0, \frac{\pi}{2}\right)\)
Step-by-step Solution
Detailed explanation
It is given that, \(y=\operatorname{cosec}^{-1} x\) \(\text {and } \frac{d y}{d x}=\frac{-1}{|x| \sqrt{x^2-1}}\) \(\because\) Domain of \(\operatorname{cosec}^{-1} x\) is \(\left[-\frac{\pi}{2}, \frac{\pi}{2}\right]-\{0\}\) and the \(\frac{d y}{d x}\) is define for…
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