AP EAMCET · Maths · Differentiation
If \(y=\sin ^{-1} x\) then \(\left(1-x^2\right) y_2-x y_1=\)
- A 0
- B 1
- C 2
- D \(2 y\)
Answer & Solution
Correct Answer
(A) 0
Step-by-step Solution
Detailed explanation
\begin{aligned} & \text { } y=\sin ^{-1} x \Rightarrow x=\sin y \Rightarrow \cos y \frac{d y}{d x}=1 \\ & \Rightarrow \frac{d y}{d x}=\sec y \Rightarrow \frac{d^2 y}{d x^2}=\sec y \tan y \frac{d y}{d x}=\frac{\sin y}{\cos ^2 y} \frac{d y}{d x} \\ & \Rightarrow\left(1-\sin ^2…
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