gamme 4x^2-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

simplify solve for partial fractions long division line

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dérivée implicite d²ydx² , y=xy²+x²y

Solution

d²ydx² =−6xy⁴−12x²y³+4y³−12x³y²+4xy²−6x⁴y+4x²y+2y(1−2xy−x²)³

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Solution steps

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y=xy²+x²y

Considérer y comme y(x)

Dérivée implicite dydx de y=xy²+x²y: y²+2xy1−2xy−x²

dydx =y²+2xy1−2xy−x²

Dérivée implicite d²ydx² de dydx =y²+2xy1−2xy−x² : −2x³dydx −2x²ydydx +2x²y−2xy²dydx +2xdydx +2xy²+2ydydx +2y+2y³(1−2xy−x²)²

d²ydx² =−2x³dydx −2x²ydydx +2x²y−2xy²dydx +2xdydx +2xy²+2ydydx +2y+2y³(1−2xy−x²)²

Remplacer dydx =y²+2xy1−2xy−x² : −6xy⁴−12x²y³+4y³−12x³y²+4xy²−6x⁴y+4x²y+2y(1−2xy−x²)³

d²ydx² =−6xy⁴−12x²y³+4y³−12x³y²+4xy²−6x⁴y+4x²y+2y(1−2xy−x²)³

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

`x`²	`x`<−2
ln(`x`+5)	`x`≥−2

sin(`x`)	`x`<0
2`x`	`x`≥0

√`x`+2	`x`<1
`xx`²−6`x`+8	`x`≥1

√`x`²−4	`x`<0
`x`³−`x`	`x`≥0

gamme 4x^2-x-3

Solution

Solution steps

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