implicit derivative of (dy)/(dx),(2x+2y)^3=8x^3+8y^3

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implicit derivative dydx , (2x+2y)³=8x³+8y³

Solution

dydx =−y(2x+y)x(x+2y)

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(2x+2y)³=8x³+8y³

Treat y as y(x)

Differentiate both sides: 3(2x+2y)²(2+2dydx )=24x²+24y²dydx

Isolate dydx : dydx =−y(2x+y)x(x+2y)

dydx =−y(2x+y)x(x+2y)

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implicit derivative of (dy)/(dx),(2x+2y)^3=8x^3+8y^3

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