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quotient rule derivative of (4x-7/(x^2+5x))

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

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quotient rule ddx (4x−7x²+5x )

Solution

−4x²+14x+35(x²+5x)²

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ddx (4x−7x²+5x )

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

=ddx (4x−7)(x²+5x)−ddx (x²+5x)(4x−7)(x²+5x)²

ddx (4x−7)=4

ddx (x²+5x)=2x+5

=4(x²+5x)−(2x+5)(4x−7)(x²+5x)²

Expand 4(x²+5x)−(2x+5)(4x−7): −4x²+14x+35

=−4x²+14x+35(x²+5x)²

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

quotient rule derivative of (4x-7/(x^2+5x))

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