Question

imple 97 If y = sin' x, show that (1 – x2)
dy
dy
- X-
dx
=o.
dr2
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Answer 1

Answer:

1^2-x^2=(1+x)(1+x)

hope this helps

Answer 2

❥CORRECT QUESTION

☞$\sf \large \: if \: y = { \sin}^{ - 1} \: show \: that \: (1 - {x}^{2} ) \frac{ {d}^{2}y }{d {x}^{2} } = 0$

Solution ♡

$\sf we \: have \: y = { \sin }^{ - 1} x \\ \\ \sf\frac{dy}{dx} = \frac{1}{ \sqrt{(1 - {x}^{2} }) } \\ \\ \sf \sqrt{(1 - {x}^{2} )} \frac{dy}{dx} = 1 \\ \\ \sf \frac{d}{dx} ( \sqrt{(1 - {x}^{2} )} . \frac{dy}{dx} ) = 0 \\ \\ \sf \ \sqrt{(1 - {x}^{2} )} .\frac{ {d}^{2}y }{dx} + \frac{dy}{dx} . \frac{d}{dx} ( \sqrt{1 - {x}^{2} )} = 0 \\ \\ \sf \sqrt{(1 - {x}^{2}) } . \frac{ {d}^{2}y }{d {x}^{2} } - \frac{dy}{dx} . \frac{2x}{2 \sqrt{1 - {x}^{2} } } = 0 \\ \\ \sf (1 - {x}^{2} ) \frac{ {d}^{2} y}{d {x}^{2} } - x \frac{dy}{?dx} = 0$

Hope it's help you ✔️