TS EAMCET · Maths · Differentiation
If the function \(y=\sin ^{-1} x\), then \(\left(1-x^2\right) \frac{d^2 y}{d x^2}\) is equal to
- A \(-x \frac{d y}{d x}\)
- B \(0\)
- C \(x \frac{d y}{d x}\)
- D \(x\left(\frac{d y}{d x}\right)^2\)
Answer & Solution
Correct Answer
(C) \(x \frac{d y}{d x}\)
Step-by-step Solution
Detailed explanation
\(\frac{d y}{d x} = \frac{1}{\sqrt{1-x^2}}\) \(\frac{d^2 y}{d x^2} = \frac{d}{dx} (1-x^2)^{-1/2} = -\frac{1}{2}(1-x^2)^{-3/2}(-2x) = x(1-x^2)^{-3/2}\)…
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