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implicit derivative of (dy)/(dx),x^{2/3}+y^{2/3}=4

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∂ ∂ x (6x⁵+9x⁶−7y⁸−5x⁶y¹⁸)

Solution

54x⁵−30x⁵y¹⁸+30x⁴

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∂ ∂ x (6x⁵+9x⁶−7y⁸−5x⁶y¹⁸)

Treat y as a constant

Apply the Sum/Difference Rule: (f±g)′=f ′±g′

=∂ ∂ x (6x⁵)+∂ ∂ x (9x⁶)−∂ ∂ x (7y⁸)−∂ ∂ x (5x⁶y¹⁸)

∂ ∂ x (6x⁵)=30x⁴

∂ ∂ x (9x⁶)=54x⁵

∂ ∂ x (7y⁸)=0

∂ ∂ x (5x⁶y¹⁸)=30y¹⁸x⁵

=30x⁴+54x⁵−0−30y¹⁸x⁵

Simplify

=54x⁵−30x⁵y¹⁸+30x⁴

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

implicit derivative of (dy)/(dx),x^{2/3}+y^{2/3}=4

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