If y = sqrt(sinx + y), then "dy"/"dx" is equal to ______.

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KollegeApply · Accepted Answer

If y = sqrt(sinx + y), then "dy"/"dx" is equal to cos/(2y - 1). Explanation: Given that: y = sqrt(sinx + y) Differentiating both sides w.r.t. x `"dy"/"dx" = 1/(2sqrt(sinx + y)) * "d"/"dx" (sin x + y) $\Rightarrow$ "dy"/"dx" = 1/(2sqrt(sinx + y)) * (cos x + "dy"/"dx") $\Rightarrow$ "dy"/"dx" = 1/(2y) * [cos x + "dy"/"dx"] $\Rightarrow$ "dy"/"dx" = cosx/(2y) + 1/(2y) * "dy"/"dx" $\Rightarrow$ "dy"/"dx" - 1/(2y) * "dy"/"dx" = cosx/(2y) $\Rightarrow$ (1 - 1/(2y))"dy"/"dx" = cosx/(2y) $\Rightarrow$ ((2y - 1)/(2y)) "dy"/"dx" = cosx/(2y) $\Rightarrow$ "dy"/"dx" = cosx/(2y) xx (2y)/(2y - 1) $\Rightarrow$ "dy"/"dx" = cosx/(2y - 1)`

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