implicit derivative of (dy)/(dx),x^3+y^3=6xy

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`x`²	`x`^□	log_□	√☐	^□√☐	≤	≥	□□	·	÷	`x`^◦	π
(☐)^′	`ddx`	∂∂`x`	∫	∫_□^□	lim	∑	∞	`θ`	(`f` ◦ `g`)	`f`(`x`)

☐²

x^☐

√☐

^□√☐

□□

log_□

θ

∞

∫

ddx

≥	≤	·	÷	`x`^◦	(☐)	\|☐\|	(`f` ◦ `g`)	`f`(`x`)	ln	`e`^☐
(☐)^′	∂∂`x`	∫_□^□	lim	∑	sin	cos	tan	cot	csc	sec

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implicit derivative dydx , x³+y³−6xy=0

Solution

dydx =−x²+2yy²−2x

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Solution steps

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x³+y³−6xy=0

Treat y as y(x)

Differentiate both sides: 3x²+3y²dydx −6(y+xdydx )=0

Isolate dydx : dydx =−x²+2yy²−2x

dydx =−x²+2yy²−2x

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