tangent of y=e^{-x}*ln(x), (1,0)

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

☐²

x^☐

√☐

^□√☐

□□

log_□

θ

∞

∫

ddx

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

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taylor ln(x²−5x)

Solution

ln(6)−76 (x+1)−3772 (x+1)²−217648 (x+1)³−12975184 (x+1)⁴+…

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Taylor Series

Taylor series of function f(x) at a is defined as:
f(x)=f(a)+f^′(a)1! (x−a)+f^′′(a)2! (x−a)²+f^′′′(a)3! (x−a)³+…

Apply the Taylor Formula

=ln(6)+ddx (ln(x²−5x))(−1)1! (x+1)+d²dx² (ln(x²−5x))(−1)2! (x+1)²+d³dx³ (ln(x²−5x))(−1)3! (x+1)³+…

Evaluate Derivatives

=ln(6)+−76 1! (x+1)+−3736 2! (x+1)²+−217108 3! (x+1)³+−1297216 4! (x+1)⁴+…

Refine

=ln(6)−76 (x+1)−3772 (x+1)²−217648 (x+1)³−12975184 (x+1)⁴+…

Tangent Line Examples

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

tangent of y=e^{-x}*ln(x), (1,0)

Solution

Solution steps

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