First slide

Derivatives

Question

$If y = \sin (7 \sin^{- 1} x) then (1 - x^{2}) y_{2} - x y_{1} =$

Moderate

A

$- 49 y$
B

$- 7 y$
C

$49 y$
D

$7 y$

Solution

$\begin{array}{l} y = \sin (7 \sin^{- 1} x) \\ \Rightarrow \sqrt{1 - x^{2}} \cdot y_{2} - \frac{2 x}{2 \sqrt{1 - x^{2}}} y_{1} = - 7 \sin (7 \sin^{- 1} x) \cdot \frac{7}{\sqrt{1 - x^{2}}} \Rightarrow (1 - x^{2}) y_{2} - x y_{1} = - 7 y (7) \\ \Rightarrow (1 - x^{2}) y_{2} - x y_{1} = - 49 y . \end{array}$

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