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בעיות פופולריות

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בעיות חשבון אינפיטסימלי פופולריות

d/(dt)(1/6 t^3)	`ddt` (16 `t`³)
integral of (xsqrt(x^2+3))	∫ (`x`√`x`²+3)`dx`
y^{''}+36y=-60sec(6t)	`y`^{′ ′}+36`y`=−60sec(6`t`)
integral of 12(y^4+4y^2+8)^2(y^3+2y)	∫ 12(`y`⁴+4`y`²+8)²(`y`³+2`y`)`dy`
integral of x-10	∫ `x`−10`dx`
integral of sec^5(θ)	∫ sec⁵(θ)`d`θ
derivative C(x)=-0.01x^2+7.2x-163	`derivative` `C`(`x`)=−0.01`x`²+7.2`x`−163
integral of sin(-4x)	∫ sin(−4`x`)`dx`
integral of 6x+3	∫ 6`x`+3`dx`
integral of 1-x	∫ 1−`xdx`
derivative (x-1)^4	`derivative` (`x`−1)⁴
integral of sec^4(xta)n^5x	∫ sec⁴(`xta`)`n`⁵`xdx`
sum from n=1 to infinity of 4/(n(n+7))	∑ _n=1^∞4`n`(`n`+7)
sum from n=2 to infinity of n/(n+2)	∑ _n=2^∞`nn`+2
derivative f(x)=(x^2+3x-2)/(x^2-5x+6)	`derivative` `f`(`x`)=`x`²+3`x`−2`x`²−5`x`+6
derivative f(x)=e^x-x^3	`derivative` `f`(`x`)=`e`^x−`x`³
y^{''}+12y^'+36y=0,y(1)=0,y^'(1)=-1	`y`^{′ ′}+12`y`^′+36`y`=0,`y`(1)=0,`y`^′(1)=−1
y^'=((x-y))/((x+2y)),y(0)=1	`y`^′=(`x`−`y`)(`x`+2`y`) ,`y`(0)=1
derivative of log_{e}(cos(4x))	`ddx` (log_e(cos(4`x`)))
integral of xln(x^5)	∫ `x`ln(`x`⁵)`dx`
integral from 0 to pi/4 of xsin(2x)	∫ ₀^π4`x`sin(2`x`)`dx`
integral from 0 to 9 of (sqrt(x)-1/3 x)	∫ ₀⁹(√`x`−13 `x`)`dx`
integral of e^{2x}cos(7x)	∫ `e`^2xcos(7`x`)`dx`
limit as z approaches 1-i of x+i(2x+y)	lim _{z→ 1−i}(`x`+`i`(2`x`+`y`))
(\partial)/(\partial x)(sin(pi(2x-y)))	∂ ∂ `x` (sin(π(2`x`−`y`)))
integral of sqrt(x^7)	∫ √`x`⁷`dx`
derivative of (1-cos(x)/(1+cos(x)))	`ddx` (1−cos(`x`)1+cos(`x`) )
integral of 1/(sqrt((25-y^2)-x^2))	∫ 1√(25−`y`²)−`x`² `dx`
laplacetransform sin(2t)+2cos(2t)+e^{-t}sin(2t)	`laplacetransform` sin(2`t`)+2cos(2`t`)+`e`^−tsin(2`t`)
y^'=3y^2	`y`^′=3`y`²
sum from n=1 to infinity of 8^nx^nn!	∑ _n=1^∞8ⁿ`x`ⁿ`n`!
(\partial)/(\partial x)((x^2+y^2)^{-1})	∂ ∂ `x` ((`x`²+`y`²)⁻¹)
x*(dy)/(dx)=xtan(y/x)+y	`x`· `dydx` =`x`tan(`yx` )+`y`
integral of x(x+8)^5	∫ `x`(`x`+8)⁵`dx`
derivative of-3cos^2(x)	`ddx` (−3cos²(`x`))
derivative y=x^3+1	`derivative` `y`=`x`³+1
derivative (6x+8x^2)/((3+8x)^2)	`derivative` 6`x`+8`x`²(3+8`x`)²
(dx)/(dt)=-2x+t	`dxdt` =−2`x`+`t`
taylor sqrt(x),\at 4	`taylor` √`x`,at 4
limit as x approaches 0 of (1-5x)^{3/x}	lim _{x→ 0}((1−5`x`)^3x)
derivative x^3csc(x)	`derivative` `x`³csc(`x`)
derivative of ln((ln(x)^2))	`ddx` (ln((ln(`x`))²))
integral of (1-sin^3(x))/(sin^2(x))	∫ 1−sin³(`x`)sin²(`x`) `dx`
derivative of (2x^2-3x+1/x)	`ddx` (2`x`²−3`x`+1`x` )
slope x^2+xy+2y^2=28,(2,3)	`slope` `x`²+`xy`+2`y`²=28,(2,3)
t^2y^{''}+7ty^'+10y=0	`t`²`y`^{′ ′}+7`ty`^′+10`y`=0
integral of tan(4x)sec^5(4x)	∫ tan(4`x`)sec⁵(4`x`)`dx`
limit as x approaches 7-of 1/(x-7)	lim _{x→ 7−}(1`x`−7 )
derivative sqrt(x^2+6)	`derivative` √`x`²+6
tangent arcsin(x/7)	`tangent` arcsin(`x`7 )
y^'=(x^2+2y^2)/(xy)	`y`^′=`x`²+2· `y`²`x`· `y`
derivative of 10xsin(x)	`ddx` (10`x`sin(`x`))
9x^2y^2+x^{3/2}y^'=y^2	9`x`²`y`²+`x`³²`y`^′=`y`²
derivative (x^2-18)(2x+3)	`derivative` (`x`²−18)(2`x`+3)
integral of x+1/(x^2)	∫ `x`+1`x`² `dx`
(\partial)/(\partial x)(xy-1)	∂ ∂ `x` (`xy`−1)
(\partial)/(\partial y)((x^2-1)(y+2))	∂ ∂ `y` ((`x`²−1)(`y`+2))
tangent f(x)= 3/(x^2),\at x=1	`tangent` `f`(`x`)=3`x`² ,at `x`=1
integral from 0 to pi/4 of 4sin^2(x)	∫ ₀^π44sin²(`x`)`dx`
limit as h approaches 0 of (1+5h)^{1/h}	lim _{h→ 0}((1+5`h`)^1h)
derivative of sqrt(y^2-x^2)	`ddx` (√`y`²−`x`²)
integral of e^{5x+e^{5x}}	∫ `e`^{5x+e^5x}`dx`
inverselaplace s/(2s^2+4s+3)	`inverselaplace` `s`2`s`²+4`s`+3
(dy)/(dx)=(xsqrt(1-y^2))/(ysqrt(1-x^2))	`dydx` =`x`√1−`y`²`y`√1−`x`²
integral of x^3-2x^{-2}+6x	∫ `x`³−2`x`⁻²+6`xdx`
taylor sqrt(9+x^2)	`taylor` √9+`x`²
derivative ln(4x^3)	`derivative` ln(4`x`³)
integral of (sqrt(x^5-1))/x	∫ √`x`⁵−1`x` `dx`
integral of 1/(sqrt(x^2-4x+8))	∫ 1√`x`²−4`x`+8 `dx`
derivative of 2x^{sqrt(x)}	`ddx` (2`x`^√x)
integral of (sqrt(2x-3))/(2x+1)	∫ √2`x`−32`x`+1 `dx`
integral of-4sin(5x)sin(x)	∫ −4sin(5`x`)sin(`x`)`dx`
derivative of 1/(1+sin(x))	`ddx` (11+sin(`x`) )
integral of 3/4 t+6	∫ 34 `t`+6`dt`
limit as x approaches 3-of sqrt(9-x^2)	lim _{x→ 3−}(√9−`x`²)
tangent f(x)=(x+2)/(x^2-9),\at x=1	`tangent` `f`(`x`)=`x`+2`x`²−9 ,at `x`=1
integral of sqrt(3x-12)	∫ √3`x`−12`dx`
derivative of 3/(2x+(4x)/5)	`ddx` (32`x` +4`x`5 )
derivative y=(3x+4)/(sqrt(2x-1))	`derivative` `y`=3`x`+4√2`x`−1
derivative f(x)=(x^6-4x^2+2)ln(x)	`derivative` `f`(`x`)=(`x`⁶−4`x`²+2)ln(`x`)
integral of 2/3 t^{3/2}-8sin(t)+C	∫ 23 `t`³²−8sin(`t`)+`Cdt`
(\partial)/(\partial x)(e^{x^2+y}-2xy)	∂ ∂ `x` (`e`^x²+y−2`xy`)
y^'=xy(y+2)	`y`^′=`xy`(`y`+2)
sum from n=1 to infinity of 9/(n^3)	∑ _n=1^∞9`n`³
sum from n=0 to infinity of 4(3/4)^n	∑ _n=0^∞4(34 )ⁿ
derivative of (ln(x+2)/(4x^{-2)})	`ddx` (ln(`x`+2)4`x`⁻² )
inverselaplace (2s+1)/(s^3)	`inverselaplace` 2`s`+1`s`³
derivative h(x)=(x^2+4x+1)/(3x+5)	`derivative` `h`(`x`)=`x`²+4`x`+13`x`+5
derivative of 5x^{2x}	`ddx` (5`x`^2x)
integral of 2x*e^{2x}	∫ 2`x`· `e`^2x`dx`
integral of (1+1/u)^{-3}(1/(u^2))	∫ (1+1`u` )⁻³(1`u`² )`du`
derivative of 4sqrt(x)+8x^{3/8}	`ddx` (4√`x`+8`x`³⁸)
derivative of sqrt(((x^2-4^3)/(36)))	`ddx` (√(`x`²−4)³36 )
limit as x approaches 1+of 1/(x^3)	lim _{x→ 1+}(1`x`³ )
slopeintercept (-5,-1),(0,3)	`slopeintercept` (−5,−1),(0,3)
(dy)/(dx)=(y+1)/(x^3)	`dydx` =`y`+1`x`³
sum from n=1 to infinity of ((3x)^n)/n	∑ _n=1^∞(3`x`)ⁿ`n`
integral of x-sqrt(x)	∫ `x`−√`xdx`
integral of (5x)/(cos^2(x^2))	∫ 5`x`cos²(`x`²) `dx`
integral of 21	∫ 21`dx`

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