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(12+8)-14

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`x`²	`x`^□	log_□	√☐	^□√☐	≤	≥	□□	·	÷	`x`^◦	π
(☐)^′	`ddx`	∂∂`x`	∫	∫_□^□	lim	∑	∞	`θ`	(`f` ◦ `g`)	`f`(`x`)

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ddx

≥	≤	·	÷	`x`^◦	(☐)	\|☐\|	(`f` ◦ `g`)	`f`(`x`)	ln	`e`^☐
(☐)^′	∂∂`x`	∫_□^□	lim	∑	sin	cos	tan	cot	csc	sec

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ddx (x+42x+6 )

Solution

−12(x+3)²

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ddx (x+42x+6 )

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

=ddx (x+4)(2x+6)−ddx (2x+6)(x+4)(2x+6)²

ddx (x+4)=1

ddx (2x+6)=2

=1· (2x+6)−2(x+4)(2x+6)²

Simplify 1· (2x+6)−2(x+4)(2x+6)² : −12(x+3)²

=−12(x+3)²

Order of operations two-step with parentheses Examples

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

(12+8)-14

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