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Use Implicit Differentiation to Determine dydx\frac { d y } { d x }

Question 42

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Use implicit differentiation to determine dydx\frac { d y } { d x } where x2y3+x=yx ^ { 2 } y ^ { 3 } + x = y . Is dydx=2xy3+13x2y2+1\frac { d y } { d x } = \frac { 2 x y ^ { 3 } + 1 } { - 3 x ^ { 2 } y ^ { 2 } + 1 } correct?

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