(\partial)/(\partial x)(19x^7+3x^2-16y^7-13x^9y^{17})

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∂ ∂ x (19x⁷+3x²−16y⁷−13x⁹y¹⁷)

Solution

−117x⁸y¹⁷+133x⁶+6x

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∂ ∂ x (19x⁷+3x²−16y⁷−13x⁹y¹⁷)

Treat y as a constant

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

=∂ ∂ x (19x⁷)+∂ ∂ x (3x²)−∂ ∂ x (16y⁷)−∂ ∂ x (13x⁹y¹⁷)

∂ ∂ x (19x⁷)=133x⁶

∂ ∂ x (3x²)=6x

∂ ∂ x (16y⁷)=0

∂ ∂ x (13x⁹y¹⁷)=117y¹⁷x⁸

=133x⁶+6x−0−117y¹⁷x⁸

Simplify

=−117x⁸y¹⁷+133x⁶+6x

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

(\partial)/(\partial x)(19x^7+3x^2-16y^7-13x^9y^{17})

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