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Question
Find `"dy"/"dx"` if `xsqrt(x) + ysqrt(y) = asqrt(a)`
Solution
`xsqrt(x) + ysqrt(y) = asqrt(a)`
∴ `x^(3/2) + y^(3/2) = a^(3/2)`
Differentiating both sides w.r.t. x, we get
`(3)/(2).x^(1/2) + (3)/(2).y^(1/2)"dy"/"dx"` = 0
∴ `(3)/(2).y^(1/2)"dy"/"dx" = -(3)/(2)x^(1/2)`
∴ `"dy"/"dx" = (-x^(1/2))/(y^(1/2)`
= `-sqrt(x/y).`
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