implicit derivative of (dy)/(dx),(4x+4y)^3=64x^3+64y^3

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

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√☐

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log_□

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(☐)^′	∂∂`x`	∫_□^□	lim	∑	sin	cos	tan	cot	csc	sec

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implicit derivative dydx , (4x+4y)³=64x³+64y³

Solution

dydx =−y(2x+y)x(x+2y)

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(4x+4y)³=64x³+64y³

Treat y as y(x)

Differentiate both sides: 3(4x+4y)²(4+4dydx )=192x²+192y²dydx

Isolate dydx : dydx =−y(2x+y)x(x+2y)

dydx =−y(2x+y)x(x+2y)

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−▭▭	<	7	8	9	÷	`AC`
+▭▭	>	4	5	6	×	☐☐☐
×▭▭	(	1	2	3	−	`x`
▭ \|▭	)	.	0	=	+	`y`

implicit derivative of (dy)/(dx),(4x+4y)^3=64x^3+64y^3

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