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implicit derivative of (dy)/(dx),x^7y^{12}+13x^5+14y^{15}=19

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(☐)^′	`ddx`	∂∂`x`	∫	∫_□^□	lim	∑	∞	`θ`	(`f` ◦ `g`)	`f`(`x`)

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implicit derivative dydx , x⁷y¹²+13x⁵+14y¹⁵=19

Solution

dydx =−7x⁶y¹²−65x⁴6y¹¹(2x⁷+35y³)

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Solution steps

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x⁷y¹²+13x⁵+14y¹⁵=19

Treat y as y(x)

Differentiate both sides: 7x⁶y¹²+12y¹¹dydx x⁷+65x⁴+210y¹⁴dydx =0

Isolate dydx : dydx =−7x⁶y¹²−65x⁴6y¹¹(2x⁷+35y³)

dydx =−7x⁶y¹²−65x⁴6y¹¹(2x⁷+35y³)

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

implicit derivative of (dy)/(dx),x^7y^{12}+13x^5+14y^{15}=19

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