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العربية

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مسائل مشهورة

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مسائل حساب التفاضل والتكامل مشهورة

(dx)/(dt)=3x^2+2x	`dxdt` =3`x`²+2`x`
integral of 5/(\sqrt[3]{x)}	∫ 5³√`x` `dx`
derivative of (arcsin(x)/(sqrt(1-x^2)))	`ddx` (arcsin(`x`)√1−`x`² )
limit as x approaches 8-of (sqrt(64-x^2))/(x-8)	lim _{x→ 8−}(√64−`x`²`x`−8 )
derivative of xsqrt(64-x^2)	`ddx` (`x`√64−`x`²)
derivative of \sqrt[3]{(3x/(x+2)})	`ddx` (³√3`xx`+2 )
derivative f(t)=(\sqrt[3]{t})/(t-3)	`derivative` `f`(`t`)=³√`tt`−3
integral from 0 to 5 of pi(25-x^2)	∫ ₀⁵π(25−`x`²)`dx`
limit as x approaches 4 of (x+3)^2	lim _{x→ 4}((`x`+3)²)
(d^2}{dx^2}(e^{-\frac{x^2)/2})	`d`²`dx`² (`e`^−x²2)
(d^3)/(dx^3)(sin(x))	`d`³`dx`³ (sin(`x`))
limit as x approaches 0+of tan(4x)	lim _{x→ 0+}(tan(4`x`))
derivative 4/(x^7)	`derivative` 4`x`⁷
derivative sqrt(18-2x)	`derivative` √18−2`x`
taylor f(x)=2^x	`taylor` `f`(`x`)=2^x
limit as x approaches-infinity of 6/((1+e^{-x))}	lim _{x→ −∞}(6(1+`e`^−x) )
limit as x approaches 7 of (x^3-4x^2-19x-14)/(x^2-8x-7)	lim _{x→ 7}(`x`³−4`x`²−19`x`−14`x`²−8`x`−7 )
y^{''}+2y^'+y=x^2-2x+1	`y`^{′ ′}+2`y`^′+`y`=`x`²−2`x`+1
derivative of (x^4ln(x)^5)	`ddx` ((`x`⁴ln(`x`))⁵)
limit as x approaches 6 of ln(6-x)	lim _{x→ 6}(ln(6−`x`))
limit as x approaches 0 of x-1/x	lim _{x→ 0}(`x`−1`x` )
limit as x approaches 0+of 4sin(x)ln(x)	lim _{x→ 0+}(4sin(`x`)ln(`x`))
derivative 1/(sqrt(1+x^2))	`derivative` 1√1+`x`²
limit as x approaches 3 of (-4)/(2x-5)	lim _{x→ 3}(−42`x`−5 )
derivative of x+6x^{2/3}	`ddx` (`x`+6`x`²³)
xy^'=xsqrt(y)+2sqrt(y)	`xy`^′=`x`√`y`+2√`y`
(d^2)/(dx^2)(sqrt(x+2))	`d`²`dx`² (√`x`+2)
integral of (x^2+1)/(sqrt(x))	∫ `x`²+1√`x` `dx`
tangent y=-1/4 x^2,(-2,-1)	`tangent` `y`=−14 `x`²,(−2,−1)
tangent (1+2x)^2	`tangent` (1+2`x`)²
y^{''}-8y^'+41y=0	`y`^{′ ′}−8`y`^′+41`y`=0
integral of (x-1)/(x(x^2-5x+6))	∫ `x`−1`x`(`x`²−5`x`+6) `dx`
integral of (3-5x)^2	∫ (3−5`x`)²`dx`
(dy)/(dx)=2ycos(x)	`dydx` =2`y`cos(`x`)
limit as x approaches 4 of-x^2-9x-8	lim _{x→ 4}(−`x`²−9`x`−8)
derivative of (5sqrt(x)/(2x^{-2)})	`ddx` (5√`x`2`x`⁻² )
limit as x approaches infinity of 3+x^2	lim _{x→ ∞}(3+`x`²)
area 2y=3sqrt(x),y=4,2y+3x=6	`area` 2`y`=3√`x`,`y`=4,2`y`+3`x`=6
integral of ((x-1))/(((x-2)(x^2-2x+2)^2))	∫ (`x`−1)((`x`−2)(`x`²−2`x`+2)²) `dx`
limit as x approaches 0+of (3x)^{sin(x)}	lim _{x→ 0+}((3`x`)^sin(x))
25y^{''}-40y^'+16y=0,y(0)=2,y^'(0)=-3	25`y`^{′ ′}−40`y`^′+16`y`=0,`y`(0)=2,`y`^′(0)=−3
integral of 5sin^3(x)cos^7(x)	∫ 5sin³(`x`)cos⁷(`x`)`dx`
integral from 1 to 2 of ln\|x^2+1\|	∫ ₁²ln\|`x`²+1\|`dx`
derivative of ln(4x-1)	`ddx` (ln(4`x`−1))
integral from 4 to 5 of 1/(5x-1)	∫ ₄⁵15`x`−1 `dx`
xy^'+3y=(4e^{2x})/(x^2)	`xy`^′+3`y`=4`e`^2x`x`²
limit as x approaches 1 of (2x)/(x-1)	lim _{x→ 1}(2`xx`−1 )
derivative f(x)=9x^5(x^3-2x)	`derivative` `f`(`x`)=9`x`⁵(`x`³−2`x`)
y^{''}-2y^'-63y=0	`y`^{′ ′}−2`y`^′−63`y`=0
sum from n=1 to infinity of 1/(n^{-1)}	∑ _n=1^∞1`n`⁻¹
(d^2y)/(d^2x)+(4dy)/(dx)+3y=0	`d`²`yd`²`x` +4`dydx` +3`y`=0
limit as x approaches 0 of x/(x^2-4)	lim _{x→ 0}(`xx`²−4 )
t^3(dy)/(dt)+3t^2y=2cos(t)	`t`³`dydt` +3`t`²`y`=2cos(`t`)
integral of x^{15}e^{-x^{16}}	∫ `x`¹⁵`e`^−x¹⁶`dx`
derivative f(t)=2t^3-3t^2-4t	`derivative` `f`(`t`)=2`t`³−3`t`²−4`t`
(\partial)/(\partial x)((4pi^2x)/(y^2))	∂ ∂ `x` (4π²`xy`² )
derivative 9xe^xcsc(x)	`derivative` 9`xe`^xcsc(`x`)
area 1/x ,1,2	`area` 1`x` ,1,2
integral of ((x^2+1))/((x-3)(x-2)^2)	∫ (`x`²+1)(`x`−3)(`x`−2)² `dx`
implicit (dy)/(dx),xy^3+10y^{11}=9	`implicit` `dydx` ,`xy`³+10`y`¹¹=9
area y^2-3x=1,x-y=3	`area` `y`²−3`x`=1,`x`−`y`=3
(dy)/(dt)=-100y+101cos(t)+99sin(t)	`dydt` =−100`y`+101cos(`t`)+99sin(`t`)
tangent y=2e^x-3x+1,\at x=0	`tangent` `y`=2`e`^x−3`x`+1,at `x`=0
derivative 4x^2-12x+5	`derivative` 4`x`²−12`x`+5
integral of-2x^2sin(pix)	∫ −2`x`²sin(π`x`)`dx`
integral of y/y	∫ `yy` `dy`
tangent f(x)=-1-2cos(x),\at x=-pi/4	`tangent` `f`(`x`)=−1−2cos(`x`),at `x`=−π4
y^'=(x-3)(y+1)^{2/3},y(0)=-1	`y`^′=(`x`−3)(`y`+1)²³,`y`(0)=−1
derivative of (2x+3/(3x^2-4))	`ddx` (2`x`+33`x`²−4 )
tangent (5x-4)^4,\at x=2	`tangent` (5`x`−4)⁴,at `x`=2
integral from 0 to 1 of e^{-x}	∫ ₀¹`e`^−x`dx`
integral of 2sin(x	∫ 2sin(`d`)`xdx`
(\partial)/(\partial x)(3sin(3x))	∂ ∂ `x` (3sin(3`x`))
integral of sin^6(x/2)	∫ sin⁶(`x`2 )`dx`
(dy)/(dx)-3y=6	`dydx` −3`y`=6
slope f(t)=16t^2	`slope` `f`(`t`)=16`t`²
integral of ln(21x)	∫ ln(21`x`)`dx`
integral of pi/(20)sin(5x)cos(8x)	∫ π20 sin(5`x`)cos(8`x`)`dx`
integral of 3tsin^2(t)	∫ 3`t`sin²(`t`)`dt`
tangent 3x^2,\at x=-1	`tangent` 3`x`²,at `x`=−1
derivative y=ln(x-3)	`derivative` `y`=ln(`x`−3)
integral of 7cos(x)cos^5(sin(x))	∫ 7cos(`x`)cos⁵(sin(`x`))`dx`
derivative of sqrt(9x+8)	`ddx` (√9`x`+8)
integral of (tan(x))/(sec(x)+4cos(x))	∫ tan(`x`)sec(`x`)+4cos(`x`) `dx`
integral of 12x+5	∫ 12`x`+5`dx`
(\partial)/(\partial x)(cos(4y^2-2x))	∂ ∂ `x` (cos(4`y`²−2`x`))
derivative of sin(x^{tan(x}))	`ddx` (sin(`x`^tan(x)))
(2x+1)y^'+2y=4x,y(0)=1	(2`x`+1)`y`^′+2`y`=4`x`,`y`(0)=1
(\partial)/(\partial z)(ln(x^2+y^4)-z)	∂ ∂ `z` (ln(`x`²+`y`⁴)−`z`)
25y^{''}-y=xe^{x/5},y(0)=1,y^'(0)=0	25`y`^{′ ′}−`y`=`xe`^x5,`y`(0)=1,`y`^′(0)=0
limit as x approaches infinity of 1/(x(ln(x))^4)	lim _{x→ ∞}(1`x`(ln(`x`))⁴ )
integral from 1 to 3 of sqrt(1+(x^3-1/(4x^3))^2)	∫ ₁³√1+(`x`³−14`x`³ )²`dx`
(\partial)/(\partial v)(sqrt(uv))	∂ ∂ `v` (√`uv`)
(\partial)/(\partial z)(2x^4yz^3)	∂ ∂ `z` (2`x`⁴`yz`³)
derivative of 3/(4x^8)	`ddx` (34`x`⁸ )
xy^'+y=6xy^2,y(1)=-4	`xy`^′+`y`=6`xy`²,`y`(1)=−4
derivative 1-2sin^3(x)	`derivative` 1−2sin³(`x`)
integral of (x^3)/(e^x)	∫ `x`³`e`^x `dx`
derivative of (4x^5+6/(x^3))	`ddx` (4`x`⁵+6`x`³ )
derivative-5/x	`derivative` −5`x`

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