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בעיות פופולריות

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בעיות חשבון אינפיטסימלי פופולריות

derivative y=arcsin(x+1)	`derivative` `y`=arcsin(`x`+1)
integral of 2/3 x^{3/2}-9sin(x)	∫ 23 `x`³²−9sin(`x`)`dx`
(\partial)/(\partial x)(7xsin(y-z))	∂ ∂ `x` (7`x`sin(`y`−`z`))
limit as x approaches 8 of (sqrt(7+\sqrt[3]{x)}-3)/(x-8)	lim _{x→ 8}(√7+³√`x`−3`x`−8 )
integral of 3x^2-2y^2	∫ 3`x`²−2`y`²`dx`
integral of x/(1-2x)	∫ `x`1−2`x` `dx`
limit as x approaches 1 of sqrt(3+f(x))	lim _{x→ 1}(√3+`f`(`x`))
integral of t^2e^{-4t}	∫ `t`²`e`^−4t`dt`
derivative of (4x/(7x-2))	`ddx` (4`x`7`x`−2 )
inverselaplace 1/((2s+1)s)	`inverselaplace` 1(2`s`+1)`s`
integral of x^2ln(9x)	∫ `x`²ln(9`x`)`dx`
derivative of (tan^2(x)/(tan(x^2)))	`ddx` (tan²(`x`)tan(`x`²) )
sqrt(x)(dy)/(dx)=e^{7y+sqrt(x)}	√`xdydx` =`e`^7y+√x
sum from n=1 to infinity of 5(-1/6)^{5n}	∑ _n=1^∞5(−16 )⁵ⁿ
derivative f(x)=(2x^2-x-1)/(2x+2)	`derivative` `f`(`x`)=2`x`²−`x`−12`x`+2
limit as x approaches 0+of x^{20x}	lim _{x→ 0+}(`x`^20x)
derivative of 7x^4cot(x)	`ddx` (7`x`⁴cot(`x`))
xydx-(1+x^2)dy=0	`xydx`−(1+`x`²)`dy`=0
x''	`x`′ ′
(dy)/(dx)+3y=40	`dydx` +3`y`=40
derivative of sqrt(x)(2x+4)	`ddx` (√`x`(2`x`+4))
limit as x approaches 7 of (x+6)/(x+1)	lim _{x→ 7}(`x`+6`x`+1 )
tangent (x^3+2x)^3,\at x=4	`tangent` (`x`³+2`x`)³,at `x`=4
integral from 0 to 2 of x^6	∫ ₀²`x`⁶`dx`
integral of xcos(4pi)x^2	∫ `x`cos(4π)`x`²`dx`
derivative of (x^2+x+2/(2x))	`ddx` (`x`²+`x`+22`x` )
area y=2x^2,y=2x+6	`area` `y`=2`x`²,`y`=2`x`+6
derivative ln(x)	`derivative` ln(`x`)
derivative of (e^x-e^{-x}/5)	`ddx` (`e`^x−`e`^−x5 )
(xdy)/(dx)=y+sqrt(x^2-y^2)	`xdydx` =`y`+√`x`²−`y`²
integral from-1/4 to 1/4 of 1/(1-x^2)	∫ ₋₁₄¹⁴11−`x`² `dx`
laplacetransform-9t^2	`laplacetransform` −9`t`²
integral of (3x)/(1+x^2)	∫ 3`x`1+`x`² `dx`
integral of (-2sqrt(x))	∫ (−2√`x`)`dx`
(\partial)/(\partial x)(x+y^3)	∂ ∂ `x` (`x`+`y`³)
(\partial)/(\partial x)(2yx-3y+y^2)	∂ ∂ `x` (2`yx`−3`y`+`y`²)
ye^{xy}dx+xe^{xy}dy=0	`ye`^xy`dx`+`xe`^xy`dy`=0
derivative of a/(bx^2)	`ddx` (`abx`² )
derivative 2x	`derivative` 2`x`
inverselaplace ((s-10))/((s^2-2s-3))	`inverselaplace` (`s`−10)(`s`²−2`s`−3)
implicit (dy)/(dx),x^6-5xy^3=9xy	`implicit` `dydx` ,`x`⁶−5`xy`³=9`xy`
limit as x approaches 0 of arctan(1/x)	lim _{x→ 0}(arctan(1`x` ))
integral of (x^2+2)/(x^3(x+1)^3)	∫ `x`²+2`x`³(`x`+1)³ `dx`
area 1/((sqrt(1-7x))),-6<x<0	`area` 1(√1−7`x`) ,−6<`x`<0
(\partial)/(\partial x)(4x^{-x^2-y^2-z^2})	∂ ∂ `x` (4`x`^{−x²−y²−z²})
integral of 7.9t-16.6	∫ 7.9`t`−16.6`dt`
derivative of 1/((1-2x^{3/2)})	`ddx` (1(1−2`x`)³² )
(\partial)/(\partial x)(x^{2/3}+y^{2/3})	∂ ∂ `x` (`x`²³+`y`²³)
integral of 1/(sqrt(64+x^2))	∫ 1√64+`x`² `dx`
f(x)=xcos(x)	`f`(`x`)=`x`cos(`x`)
derivative of ln(x+2x)	`ddx` (ln(`x`)+2`x`)
taylor 1/(1+x^2),0	`taylor` 11+`x`² ,0
integral from 0 to 1 of (1-x^7)^2	∫ ₀¹(1−`x`⁷)²`dx`
derivative x^3-2x^2-4x+6	`derivative` `x`³−2`x`²−4`x`+6
y^{''}-2y^'=x+2e^x,y(0)=18,y^'(0)= 31/4	`y`^{′ ′}−2`y`^′=`x`+2`e`^x,`y`(0)=18,`y`^′(0)=314
derivative of 2cos(x+3sin(x))	`ddx` (2cos(`x`)+3sin(`x`))
inverselaplace (s+3)/(s^2+2s+2)	`inverselaplace` `s`+3`s`²+2`s`+2
tangent 5x^2+8x-8	`tangent` 5`x`²+8`x`−8
d/(du)(sqrt(u))	`ddu` (√`u`)
derivative of (6x-1(5x-2)^{-1})	`ddx` ((6`x`−1)(5`x`−2)⁻¹)
derivative of 2(x-1^2)	`ddx` (2(`x`−1)²)
y^{''}+4y^'+5y=-10x+3e^{-x}	`y`^{′ ′}+4`y`^′+5`y`=−10`x`+3`e`^−x
limit as x approaches 3 of sqrt(x-2)	lim _{x→ 3}(√`x`−2)
integral of (sec^2(x))/x	∫ sec²(`x`)`x` `dx`
derivative f(x)=(x+5)/(x-5)	`derivative` `f`(`x`)=`x`+5`x`−5
limit as x approaches-2 of x^2-4/(x+2)	lim _{x→ −2}(`x`²−4`x`+2 )
area y=cos(x),y=0.5,0<= x<= pi	`area` `y`=cos(`x`),`y`=0.5,0≤ `x`≤ π
1296y^{''}+1368y^'+361y=0	1296`y`^{′ ′}+1368`y`^′+361`y`=0
x(dy)/(dx)=y+(x^2-2)^2	`xdydx` =`y`+(`x`²−2)²
integral of sin^2(pix)cos^5(pix)	∫ sin²(π`x`)cos⁵(π`x`)`dx`
derivative \sqrt[3]{6+2x+x^3}	`derivative` ³√6+2`x`+`x`³
derivative of csc^2(1-2x)	`ddx` (csc²(1−2`x`))
limit as x approaches-1 of 3x^4-6x+1	lim _{x→ −1}(3`x`⁴−6`x`+1)
integral of 3x^2+2x	∫ 3`x`²+2`xdx`
limit as x approaches 2 of x^3-5x	lim _{x→ 2}(`x`³−5`x`)
limit as x approaches-6+of sqrt(x+6)	lim _{x→ −6+}(√`x`+6)
derivative of 3\sqrt[3]{x^2}-2x	`ddx` (3³√`x`²−2`x`)
integral of 1/(sqrt(cos(x)+cos^2(x)))	∫ 1√cos(`x`)+cos²(`x`) `dx`
(\partial)/(\partial z)(ln(1+xy)-z)	∂ ∂ `z` (ln(1+`xy`)−`z`)
derivative f(x)=sqrt(x+8)	`derivative` `f`(`x`)=√`x`+8
integral of tln(1+t)	∫ `t`ln(1+`t`)`dt`
integral from-8 to 0 of (y/8+sqrt(y+9))	∫ ₋₈⁰(`y`8 +√`y`+9)`dy`
limit as x approaches infinity of x+9	lim _{x→ ∞}(`x`+9)
integral of 1/(x^2+3x+3)	∫ 1`x`²+3`x`+3 `dx`
y''(x)-3y'(x)+2y= 1/(1+e^{-x)}	`y`′ ′ (`x`)−3`y`′ (`x`)+2`y`=11+`e`^−x
limit as x approaches 0 of-arcsin(x)	lim _{x→ 0}(−arcsin(`x`))
derivative of 5e^x+2/(\sqrt[3]{x})	`ddx` (5`e`^x+2³√`x` )
integral from 0 to 1 of 9cos((pit)/2)	∫ ₀¹9cos(π`t`2 )`dt`
integral of 1/(sqrt(x^2+36))	∫ 1√`x`²+36 `dx`
derivative ln(3)	`derivative` ln(3)
derivative of ln(1/(1-x))	`ddx` (ln(11−`x` ))
area y=4x^2,y=x^2+6	`area` `y`=4`x`²,`y`=`x`²+6
limit as x approaches 7 of x+2	lim _{x→ 7}(`x`+2)
integral of xe^xln(x-1)	∫ `xe`^xln(`x`−1)`dx`
integral of (sin^5(ln(x)))/x	∫ sin⁵(ln(`x`))`x` `dx`
limit as x approaches 0 of (sqrt(5+x)-sqrt(5))/(2x)	lim _{x→ 0}(√5+`x`−√52`x` )
derivative f(t)=e^{7tsin(2t)}	`derivative` `f`(`t`)=`e`^7tsin(2t)
tangent f(x)=x(27x^{-2}+2),\at x=-3	`tangent` `f`(`x`)=`x`(27`x`⁻²+2),at `x`=−3
(\partial)/(\partial x)((x-1)/(x+1))	∂ ∂ `x` (`x`−1`x`+1 )
integral from 0 to infinity of 1/(e^x-1)	∫ ₀^∞1`e`^x−1 `dx`

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