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implicit derivative of (dy)/(dx),x^{13}-y^5=4xy

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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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Steps Examples

Generated by AI

inverse (

1	5	7	9
0	2	6	8
2	6	3	7
5	2	3	4

)

Solution

(

−9134	−7268	−1134	29134
45134	−99268	5134	−11134
77134	−89268	−51134	5134
−69134	125268	37134	−1134

)

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Solution steps

One step at a time

(

1	5	7	9
0	2	6	8
2	6	3	7
5	2	3	4

)⁻¹

Inverse matrix

A matrix is invertible if and only if there is a sequence of elementary row (or column) operations taking it to the identity matrix.

Augment with a 4x4 identity matrix

[

1	5	7	9	∣	1	0	0	0
0	2	6	8	∣	0	1	0	0
2	6	3	7	∣	0	0	1	0
5	2	3	4	∣	0	0	0	1

]

Reduce the matrix on the left to the identity matrix

[

1	0	0	0	∣	−9134	−7268	−1134	29134
0	1	0	0	∣	45134	−99268	5134	−11134
0	0	1	0	∣	77134	−89268	−51134	5134
0	0	0	1	∣	−69134	125268	37134	−1134

]

The inverse matrix is on the right side of the augmented matrix

−9134	−7268	−1134	29134
45134	−99268	5134	−11134
77134	−89268	−51134	5134
−69134	125268	37134	−1134

)

Order of operations three/four steps without parentheses Examples

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1	5	7	9
0	2	6	8
2	6	3	7
5	2	3	4

) or choose below

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

implicit derivative of (dy)/(dx),x^{13}-y^5=4xy

Solution

Solution steps

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