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If y = sqrt(sin + y ) "then" (dy)/(dx) ...

If ` y = sqrt(sin + y ) "then" (dy)/(dx) ` is equal to

A

`(cos x )/(2y -1)`

B

`(cos x )/(1 - 2y)`

C

`(sin x )/(1 - 2y)`

D

`(sin x)/(2y - 1)`

Text Solution

Verified by Experts

The correct Answer is:
A
Given , ` y = (sin x + y)^(1//2)`
On differentiating both sides of Eq .(i) w.r.t.x, we get
`rarr (dy)/(dt) = (1)/(2) .(1)/((sin x + y)^(1//2)).(cos x + (dy)/(dx))`
` rArr (dy)/(dx) = (1)/(2y) (cos x + (dy)/(dx) ) [ because (sin x + y )^(1//2) = y]`
`rArr (dy)/(dx) (1 - (1)/(2y)) = (cos x )/(2y)`
` therefore (dy)/(dx)= (cos x)/(2y) .(2y)/(2y-1) = (cos x )/(2y -1)`
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MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS-DIFFERENTIATION -EXERCISE 1 DERIVATIVE OF COMPOSITE FUNCTION (BY CHAIN RULE )
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  12. If x=(1-sqrt(y))/(1+sqrt(y)) then (dy)/(dx) is equal to

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  13. If y = log (sin (x^(2))), 0 lt x lt (pi)/(2), "then " (dy)/(dx) "at ...

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