AP EAMCET · Maths · Differentiation
If \(y=\sin \left(m \sin ^{-1} x\right)\), then \(\left(1-x^2\right) y_2-x y_1\) is equal to \(\left(\right.\) Here, \(y_n\) denotes \(\left.\frac{d^n y}{d x^n}\right)\)
- A \(m^2 y\)
- B \(-m^2 y\)
- C \(2 m^2 y\)
- D \(-2 m^2 y\)
Answer & Solution
Correct Answer
(B) \(-m^2 y\)
Step-by-step Solution
Detailed explanation
\(y=\sin \left(m \sin ^{-1} x\right)\) \(y_1=\cos \left(m \sin ^{-1} x\right) \cdot m \cdot \frac{1}{\sqrt{1-x^2}}\) where \(\left(y_1=\frac{d y}{d x}\right)\) \(y_1 \sqrt{1-x^2}=m \cos \left(m \sin ^{-1} x\right)\)…
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