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Question
If y = sin–1x, then (1 – x2)y2 is equal to ______.
Options
xy1
xy
xy2
x2
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Solution
If y = sin–1x, then (1 – x2)y2 is equal to `underline(bb(xy_1))`.
Explanation:
y = sin–1x
`(dy)/(dx) = 1/sqrt(1 - x^2)`
⇒ `sqrt(1 - x^2) . (dy)/(dx)` = 1
Again, differentiating both sides w. r. to x, we get
`sqrt(1 - x^2) (d^2y)/(dx^2) + (dy)/(dx) . ((-2x)/(2sqrt(1 - x^2)))` = 0
Simplifying, we get (1 – x2)y2 = xy1
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