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בעיות פופולריות

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בעיות חשבון אינפיטסימלי פופולריות

derivative f(x)=-x^{4/3}	`derivative` `f`(`x`)=−`x`⁴³
integral from-1 to 1 of (8-8x^2)^2	∫ ₋₁¹(8−8`x`²)²`dx`
(\partial)/(\partial x)(y^2cos(xy))	∂ ∂ `x` (`y`²cos(`xy`))
integral of acos(x)	∫ `a`cos(`x`)`dx`
integral from 1 to 4 of 1/(4-sqrt(x))	∫ ₁⁴14−√`x` `dx`
integral of 4x(x^2+28000)^{-2/3}	∫ 4`x`(`x`²+28000)⁻²³`dx`
tangent f(x)=5x^2-4x-2,\at x=(1-1)	`tangent` `f`(`x`)=5`x`²−4`x`−2,at `x`=(1−1)
integral from-3 to 0 of x/(sqrt(9-x^2))	∫ ₋₃⁰`x`√9−`x`² `dx`
area y=sqrt(x),y= 1/3 x,x=25	`area` `y`=√`x`,`y`=13 `x`,`x`=25
integral of (sqrt(x^2+16))/(2x)	∫ √`x`²+162`x` `dx`
integral from 0 to 8 of 1/((10-2x)^{1/5)}	∫ ₀⁸1(10−2`x`)¹⁵ `dx`
integral from 0 to infinity of e^{-x}	∫ ₀^∞`e`^−x`dx`
integral of 1/(1-e^x)	∫ 11−`e`^x `dx`
limit as n approaches infinity of ln(n)	lim _{n→ ∞}(ln(`n`))
integral of (36)/(x^3-6x^2)	∫ 36`x`³−6`x`² `dx`
integral of e^{9x+7}	∫ `e`^9x+7`dx`
derivative of e^{3x+9}	`ddx` (`e`^3x+9)
tangent (x^3-9x)^{10}(3)	`tangent` (`x`³−9`x`)¹⁰(3)
((2x)/(x^2+1))^'	(2`xx`²+1 )^′
limit as x approaches 4 of 4x^2-5x+1	lim _{x→ 4}(4`x`²−5`x`+1)
derivative ln(x+3)	`derivative` ln(`x`+3)
derivative sqrt(2x^2+7)	`derivative` √2`x`²+7
y^'-2y=-1,y(0)=3	`y`^′−2`y`=−1,`y`(0)=3
(y-x)e^x+(1+e^x)y^'=0	(`y`−`x`)`e`^x+(1+`e`^x)`y`^′=0
derivative 10+(50t)/(2t^2+9)	`derivative` 10+50`t`2`t`²+9
limit as x approaches-2 of 1/2	lim _{x→ −2}(12 )
inverselaplace (-3e^{6-3s})/((s-2)(s-3)(s+2))	`inverselaplace` −3`e`^6−3s(`s`−2)(`s`−3)(`s`+2)
limit as h approaches 0 of (x+h)^3-x^3	lim _{h→ 0}((`x`+`h`)³−`x`³)
(\partial)/(\partial t)(2e^{sin(x+2ct)})	∂ ∂ `t` (2`e`^sin(x+2ct))
(dx)/(dt)=-2x	`dxdt` =−2`x`
integral of cos^2(2t)	∫ cos²(2`t`)`dt`
y^{''}+9=0	`y`^{′ ′}+9=0
derivative-2pisin(4pix)	`derivative` −2πsin(4π`x`)
derivative of 230-8x+0.04x^2	`ddx` (230−8`x`+0.04`x`²)
derivative of (csc(x*tan(x))/(cos(x)))	`ddx` (csc(`x`)· tan(`x`)cos(`x`) )
(\partial)/(\partial x)((1-x^2-y^2)^{1/2})	∂ ∂ `x` ((1−`x`²−`y`²)¹²)
limit as x approaches pi/2+of 9/x sec(x)	lim _{x→ π2 +}(9`x` sec(`x`))
(\partial)/(\partial y)(e^zcos(y))	∂ ∂ `y` (`e`^zcos(`y`))
tangent f(x)=(10)/(1+e^{-x)},\at x=0	`tangent` `f`(`x`)=101+`e`^−x ,at `x`=0
sum from n=2 to infinity of ((n+1)/n)^n	∑ _n=2^∞(`n`+1`n` )ⁿ
integral of (5^x)/(1+5^x)	∫ 5^x1+5^x `dx`
derivative of (1000+x^{-1/3})	`ddx` ((1000+`x`)⁻¹³)
integral of csc^2(x)cot^2(x)	∫ csc²(`x`)cot²(`x`)`dx`
integral of 6x^2tan(x^3)	∫ 6`x`²tan(`x`³)`dx`
implicit (dy)/(dx),16x^2-16xy+y^2=1	`implicit` `dydx` ,16`x`²−16`xy`+`y`²=1
tangent f(x)=(x^3-9x)^8,(-3,0)	`tangent` `f`(`x`)=(`x`³−9`x`)⁸,(−3,0)
(dy)/(dx)+3y=2x	`dydx` +3`y`=2`x`
area x^3,x,0,1	`area` `x`³,`x`,0,1
limit as x approaches 4 of 9/(9-(-3))	lim _{x→ 4}(99−(−3) )
limit as x approaches 0 of x^2*ln(x)	lim _{x→ 0}(`x`²· ln(`x`))
derivative of (x-pi^2)	`ddx` ((`x`−π)²)
integral from 1 to 2 of 1/(x^2)	∫ ₁²1`x`² `dx`
derivative of 4*sin(x)	`ddx` (4· sin(`x`))
maclaurin sin(x^2), pi/4	`maclaurin` sin(`x`²),π4
sum from n=1 to infinity of n*(4/5)^n	∑ _n=1^∞`n`· (45 )ⁿ
limit as x approaches 0+of x(ln(x))	lim _{x→ 0+}(`x`(ln(`x`)))
tangent 4x^2-3x+2	`tangent` 4`x`²−3`x`+2
integral from 1 to 3 of x^4	∫ ₁³`x`⁴`dx`
f^'(x)=2x+3x^{1.7}	`f`^′(`x`)=2`x`+3`x`^1.7
derivative of 1/(x(ln(x)^{2/3)})	`ddx` (1`x`(ln(`x`))²³ )
d/(dθ)((sin(θ))/(1+cos(θ)))	`dd`θ (sin(θ)1+cos(θ) )
(\partial)/(\partial z)(2xz^2cos(y))	∂ ∂ `z` (2`xz`²cos(`y`))
limit as x approaches 0 of (x^2)/(x+1)	lim _{x→ 0}(`x`²`x`+1 )
integral of sin^3(x)cos^{16}(x)	∫ sin³(`x`)cos¹⁶(`x`)`dx`
limit as y approaches 0 of (x^y-1)/y	lim _{y→ 0}(`x`^y−1`y` )
derivative 8sqrt(8x^2+5)	`derivative` 8√8`x`²+5
limit as x approaches 0-of 4/(sin(x))	lim _{x→ 0−}(4sin(`x`) )
integral of xe^{-ax^2}	∫ `xe`^−ax²`dx`
y^'=4e^{x+y}	`y`^′=4`e`^x+y
derivative 4x^2-5x	`derivative` 4`x`²−5`x`
(\partial)/(\partial x)(sin(xe^{x^2y}))	∂ ∂ `x` (sin(`x`· `e`^{x²· y}))
integral of (sin^3(2t))sqrt(cos(2t))	∫ (sin³(2`t`))√cos(2`t`)`dt`
limit as x approaches 9+of ln(x^2-81)	lim _{x→ 9+}(ln(`x`²−81))
integral of e^xsqrt(6-e^x)	∫ `e`^x√6−`e`^x`dx`
(3x^2)^'	(3`x`²)^′
integral of (x^2)/(sqrt(x^6+1))	∫ `x`²√`x`⁶+1 `dx`
integral of (20)/(x+5)	∫ 20`x`+5 `dx`
slopeintercept (2,1),(8,7)	`slopeintercept` (2,1),(8,7)
derivative (f(x))^{g(x)}	`derivative` (`f`(`x`))^g(x)
taylor e^{-x/2}0	`taylor` `e`^−x20
derivative f(x)=ln(x+sqrt(x^2+1))	`derivative` `f`(`x`)=ln(`x`+√`x`²+1)
derivative of x^2sin(x+2)	`ddx` (`x`²sin(`x`)+2)
integral of 1/(\sqrt[5]{e^{2t)}}	∫ 1⁵√`e`^2t `dt`
integral of (7+e)	∫ (7+`e`)`dx`
integral from 1 to infinity of (ln(x))/x	∫ ₁^∞ln(`x`)`x` `dx`
derivative of x^4-1/x	`ddx` (`x`⁴−1`x` )
limit as x approaches 4 of x^2-4x+1	lim _{x→ 4}(`x`²−4`x`+1)
derivative f(x)=sqrt(3x-5)	`derivative` `f`(`x`)=√3`x`−5
integral of (16x^2)/((x-9)(x+3)^2)	∫ 16`x`²(`x`−9)(`x`+3)² `dx`
derivative of (5x-4(2x^3-x^2+1))	`ddx` ((5`x`−4)(2`x`³−`x`²+1))
tangent f(x)= 1/(4+3x),(1, 1/7)	`tangent` `f`(`x`)=14+3`x` ,(1,17 )
derivative e^{9sqrt(x)}	`derivative` `e`^9√x
derivative f(x)=2x^2-4x+1	`derivative` `f`(`x`)=2`x`²−4`x`+1
integral of 1/(x^{5/8)-x^{1/8}}	∫ 1`x`⁵⁸−`x`¹⁸ `dx`
integral of 31arctan(sqrt(x))	∫ 31arctan(√`x`)`dx`
integral from 1 to 4 of 3x^{1/3}	∫ ₁⁴3`x`¹³`dx`
derivative of log_{2}(7x^2+x-2)	`ddx` (log₂(7`x`²+`x`−2))
derivative of 12x-x^2	`ddx` (12`x`−`x`²)
limit as x approaches 1 of ((x+1))/(x-1)	lim _{x→ 1}((`x`+1)`x`−1 )
derivative of x^2-1/8 ln(x)	`ddx` (`x`²−18 ln(`x`))

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