derivative of log

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

☐²

x^☐

√☐

^□√☐

□□

log_□

θ

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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 (log₄(4x))

Solution

12ln(2)x

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Solution steps

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ddx (log₄(4x))

Simplify log₄(4x): log₄(x)+1

=ddx (log₄(x)+1)

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

=ddx (log₄(x))+ddx (1)

ddx (log₄(x))=12ln(2)x

ddx (1)=0

=12ln(2)x +0

Simplify

=12ln(2)x

Log Product Rule Examples

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

derivative of log_{4}(4x)

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