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range of sqrt(x+3)

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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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d⁴dx⁴ (e^xⁿ)

Solution

n(n³e^xⁿx⁴ⁿ⁻⁴+6n³e^xⁿx³ⁿ⁻⁴+7n³e^xⁿx²ⁿ⁻⁴−6n²e^xⁿx³ⁿ⁻⁴−18n²e^xⁿx²ⁿ⁻⁴+11ne^xⁿx²ⁿ⁻⁴+n³e^xⁿxⁿ⁻⁴−6n²e^xⁿxⁿ⁻⁴+11ne^xⁿxⁿ⁻⁴−6e^xⁿxⁿ⁻⁴)

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d⁴dx⁴ (e^xⁿ)

ddx (e^xⁿ)=e^xⁿnxⁿ⁻¹

=d³dx³ (e^xⁿnxⁿ⁻¹)

ddx (e^xⁿnxⁿ⁻¹)=n(ne^xⁿx²ⁿ⁻²+e^xⁿxⁿ⁻²(n−1))

=d²dx² (n(ne^xⁿx²ⁿ⁻²+e^xⁿxⁿ⁻²(n−1)))

ddx (n(ne^xⁿx²ⁿ⁻²+e^xⁿxⁿ⁻²(n−1)))=n(n²e^xⁿx³ⁿ⁻³+3n²e^xⁿx²ⁿ⁻³−3ne^xⁿx²ⁿ⁻³+n²e^xⁿxⁿ⁻³−3ne^xⁿxⁿ⁻³+2e^xⁿxⁿ⁻³)

=ddx (n(n²e^xⁿx³ⁿ⁻³+3n²e^xⁿx²ⁿ⁻³−3ne^xⁿx²ⁿ⁻³+n²e^xⁿxⁿ⁻³−3ne^xⁿxⁿ⁻³+2e^xⁿxⁿ⁻³))

ddx (n(n²e^xⁿx³ⁿ⁻³+3n²e^xⁿx²ⁿ⁻³−3ne^xⁿx²ⁿ⁻³+n²e^xⁿxⁿ⁻³−3ne^xⁿxⁿ⁻³+2e^xⁿxⁿ⁻³))=n(n³e^xⁿx⁴ⁿ⁻⁴+6n³e^xⁿx³ⁿ⁻⁴+7n³e^xⁿx²ⁿ⁻⁴−6n²e^xⁿx³ⁿ⁻⁴−18n²e^xⁿx²ⁿ⁻⁴+11ne^xⁿx²ⁿ⁻⁴+n³e^xⁿxⁿ⁻⁴−6n²e^xⁿxⁿ⁻⁴+11ne^xⁿxⁿ⁻⁴−6e^xⁿxⁿ⁻⁴)

=n(n³e^xⁿx⁴ⁿ⁻⁴+6n³e^xⁿx³ⁿ⁻⁴+7n³e^xⁿx²ⁿ⁻⁴−6n²e^xⁿx³ⁿ⁻⁴−18n²e^xⁿx²ⁿ⁻⁴+11ne^xⁿx²ⁿ⁻⁴+n³e^xⁿxⁿ⁻⁴−6n²e^xⁿxⁿ⁻⁴+11ne^xⁿxⁿ⁻⁴−6e^xⁿxⁿ⁻⁴)

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

range of sqrt(x+3)

Solution

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