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anonymous
 5 years ago
Find dy/dx by implicit differentiation. for: x^4(x+y) = y^2(3xy)
anonymous
 5 years ago
Find dy/dx by implicit differentiation. for: x^4(x+y) = y^2(3xy)

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anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0\[\frac{d}{dx}(x^4(x+y))=\frac{d}{dx}(y^2(3xy))\]For the lefthand side:\[\rightarrow x^4\frac{d}{dx}(x+y)+(x+y)\frac{d}{dx}x^4=x^4(1+\frac{dy}{dx})+(x+y)4x^3\]\[=x^4\frac{dy}{dx}+5x^4+4x^3y\]and for the righthand side,\[y^2\frac{d}{dx}(3xy)+(3xy)\frac{d}{dx}y^2=y^2(3\frac{dy}{dx})+(3xy)2y \frac{dy}{dx}\]\[=3y^2+3y(2xy)\frac{dy}{dx}\]Hence, equating LHS and RHS:\[x^4\frac{dy}{dx}+5x^4+4x^3y=3y^2+3y(2xy)\frac{dy}{dx}\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Now you can solve for dy/dx:\[\frac{dy}{dx}=\frac{3y^25x^44x^3y}{x^46xy3y^2}\]
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