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implicit derivative of (dy)/(dx),x^3+y^3-6xy=0

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

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ddx

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

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∂ ∂ x (x−3xt+16 )

Solution

3t+16(xt+16)²

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∂ ∂ x (x−3xt+16 )

Treat t as a constant

Apply the Quotient Rule: (fg )^′=f ′·g−g′·fg²

=∂ ∂ x (x−3)(xt+16)−∂ ∂ x (xt+16)(x−3)(xt+16)²

∂ ∂ x (x−3)=1

∂ ∂ x (xt+16)=t

=1· (xt+16)−t(x−3)(xt+16)²

Simplify 1· (xt+16)−t(x−3)(xt+16)² : 3t+16(xt+16)²

=3t+16(xt+16)²

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

implicit derivative of (dy)/(dx),x^3+y^3-6xy=0

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