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(\partial)/(\partial x)(ln(x^{12}-y^8))

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∂ ∂ x (15+17x⁵+x+y⁷−y)

Solution

85x⁴+1

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Solution steps

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∂ ∂ x (15+17x⁵+x+y⁷−y)

Treat y as a constant

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

=∂ ∂ x (15)+∂ ∂ x (17x⁵)+∂ ∂ x (x)+∂ ∂ x (y⁷)−∂ ∂ x (y)

∂ ∂ x (15)=0

∂ ∂ x (17x⁵)=85x⁴

∂ ∂ x (x)=1

∂ ∂ x (y⁷)=0

∂ ∂ x (y)=0

=0+85x⁴+1+0−0

Simplify

=85x⁴+1

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

(\partial)/(\partial x)(ln(x^{12}-y^8))

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