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常见问题

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常见微积分问题

derivative e^{4z}-4e^{-4z}	`derivative` `e`^4z−4`e`^−4z
(\partial)/(\partial y)(sin(x)sin(y))	∂ ∂ `y` (sin(`x`)sin(`y`))
(x+y)dx-(x-y)dy=0,y(1)=0	(`x`+`y`)`dx`−(`x`−`y`)`dy`=0,`y`(1)=0
integral of s/(s^2+6s+11)	∫ `ss`²+6`s`+11 `ds`
derivative f(x)=sqrt(4x-3)	`derivative` `f`(`x`)=√4`x`−3
integral of-2cos(2x)	∫ −2cos(2`x`)`dx`
limit as x approaches 4/pi of cos(x)	lim _{x→ 4π}(cos(`x`))
derivative of \sqrt[3]{x}-6/x	`ddx` (³√`x`−6`x` )
derivative of 1/8 x^8-x^4	`ddx` (18 `x`⁸−`x`⁴)
derivative ln(x^2-4x)	`derivative` ln(`x`²−4`x`)
(arcsin((2x)/(1+x^2)))^'	(arcsin(2`x`1+`x`² ))^′
derivative x^4+x^3+2	`derivative` `x`⁴+`x`³+2
(\partial)/(\partial x)(sin(y)cos(x))	∂ ∂ `x` (sin(`y`)cos(`x`))
tangent-8x^2+5	`tangent` −8`x`²+5
integral of (4t)/(sqrt(1-16t^4))	∫ 4`t`√1−16`t`⁴ `dt`
integral of sin(t)sec^5(t)	∫ sin(`t`)sec⁵(`t`)`dt`
limit as x approaches 0 of (x)x	lim _{x→ 0}((`x`)`x`)
integral of arccos(sqrt((1+x)/2))	∫ arccos(√1+`x`2 )`dx`
integral of 1/(sqrt(1+u^2))	∫ 1√1+`u`² `du`
面积 y=x^2,y=x+6	`area` `y`=`x`²,`y`=`x`+6
derivative of-ln(-x)	`ddx` (−ln(−`x`))
derivative f(x)=(e^x)/(2x+1)	`derivative` `f`(`x`)=`e`^x2`x`+1
y^{''}+11y^'+30y=0	`y`^{′ ′}+11`y`^′+30`y`=0
extreme f(x,y)=sqrt(x^2+y^2)	`extreme` `f`(`x`,`y`)=√`x`²+`y`²
derivative ln(16x)	`derivative` ln(16`x`)
derivative y=a^x	`derivative` `y`=`a`^x
tangent f(x)=3-4x^2,(2,-13)	`tangent` `f`(`x`)=3−4`x`²,(2,−13)
derivative ln(1/x)	`derivative` ln(1`x` )
integral of (x+1)/(2+4x^2)	∫ `x`+12+4`x`² `dx`
derivative of x^3cot(x)	`ddx` (`x`³cot(`x`))
integral of ((sin(sqrt(w))))/(sqrt(w))	∫ (sin(√`w`))√`w` `dw`
inverselaplace ((s-2))/((s-2)^2-3)	`inverselaplace` (`s`−2)(`s`−2)²−3
integral of ((e^x))/(1+e^x)	∫ (`e`^x)1+`e`^x `dx`
derivative y=4tsqrt(t+7)	`derivative` `y`=4`t`√`t`+7
integral from-2 to 2 of x^2-1	∫ ₋₂²`x`²−1`dx`
derivative f(x)=2e^{-x}	`derivative` `f`(`x`)=2`e`^−x
integral of 4sin^4(x)cos^2(x)	∫ 4sin⁴(`x`)cos²(`x`)`dx`
泰勒 1/(2+5x)	`taylor` 12+5`x`
(dy)/(dx)=y^2-9	`dydx` =`y`²−9
derivative of 5x^3+x^2+1/x	`ddx` (5`x`³+`x`²+1`x` )
derivative of 2(5-9x^5)	`ddx` (2(5−9`x`)⁵)
integral of (1-x)/(1-x^2)	∫ 1−`x`1−`x`² `dx`
integral from 0 to 2 of (x^2-2x)	∫ ₀²(`x`²−2`x`)`dx`
integral of sin^2(x+4)	∫ sin²(`x`+4)`dx`
integral from 1 to infinity of xe^{-4x}	∫ ₁^∞`xe`^−4x`dx`
integral of sin^4(4θ)	∫ sin⁴(4θ)`d`θ
integral of ((16)/(1+x^2))	∫ (161+`x`² )`dx`
derivative sin(x^2)	`derivative` sin(`x`²)
derivative of x*e^{4x}	`ddx` (`x`· `e`^4x)
integral of ((x+2))/(x^2+3x-4)	∫ (`x`+2)`x`²+3`x`−4 `dx`
integral of ((e^{sqrt(x)}-3))/(sqrt(x))	∫ (`e`^√x−3)√`x` `dx`
integral of cos(nt)	∫ cos(`nt`)`dt`
derivative of x^3(x-4)	`ddx` (`x`³(`x`−4))
derivative 91-90e^{-0.2t}	`derivative` 91−90`e`^−0.2t
inverselaplace 6/s+16*1/(s^2+16)	`inverselaplace` 6`s` +16· 1`s`²+16
tangent f(x)= 2/(4-x),\at x=-1	`tangent` `f`(`x`)=24−`x` ,at `x`=−1
(sin^2(x))^'	(sin²(`x`))^′
derivative of 4x^{1/3}	`ddx` (4`x`¹³)
面积 5x-x^2,0	`area` 5`x`−`x`²,0
limit as h approaches 0 of h	lim _{h→ 0}(`h`)
2x^2y+x^3((dy)/(dx))=1	2`x`²`y`+`x`³(`dydx` )=1
derivative f(x)=(ln(sqrt(x)))/x	`derivative` `f`(`x`)=ln(√`x`)`x`
limit as x approaches 0 of (e^{2x}-5x)^2	lim _{x→ 0}((`e`^2x−5`x`)²)
integral of 9/(x(x^4+8))	∫ 9`x`(`x`⁴+8) `dx`
tangent y=(5x)/(x+4),(1,1)	`tangent` `y`=5`xx`+4 ,(1,1)
integral of (cos(x))/(sin(2x))	∫ cos(`x`)sin(2`x`) `dx`
泰勒 1/(x^2),2	`taylor` 1`x`² ,2
(2x^2y+2sqrt(1+x^4y^2))dx+x^3dy=0	(2`x`²`y`+2√1+`x`⁴`y`²)`dx`+`x`³`dy`=0
derivative of (4x+3^4(x+1)^{-3})	`ddx` ((4`x`+3)⁴(`x`+1)⁻³)
(dq)/(dt)+1/(5*10^{-9)}q= 200/1000	`dqdt` +15· 10⁻⁹ `q`=2001000
integral of ((ln^6(x)))/x	∫ (ln⁶(`x`))`x` `dx`
derivative of e^{(x+y}-1)	`ddx` (`e`^(x+y)−1)
tangent f(x)=(1+5x)^9,(0,1)	`tangent` `f`(`x`)=(1+5`x`)⁹,(0,1)
泰勒 e^{-x},1	`taylor` `e`^−x,1
(\partial)/(\partial x)((cos(x))^2)	∂ ∂ `x` ((cos(`x`))²)
tangent-1/((x-6)^2)	`tangent` −1(`x`−6)²
integral of csc(4x)	∫ csc(4`x`)`dx`
derivative of arcsinh(x)	`ddx` (arcsinh(`x`))
d/(dt)(\sqrt[3]{t}(t^2+4))	`ddt` (³√`t`(`t`²+4))
integral of-4/(x^2)	∫ −4`x`² `dx`
(dy)/(dx)= y/(y^2),y(0)=2	`dydx` =`yy`² ,`y`(0)=2
sum from n=1 to infinity of 1/(2+sin(n))	∑ _n=1^∞12+sin(`n`)
derivative of e^{14x}	`ddx` (`e`^14x)
integral of (x^2)/(\sqrt[3]{1+2x)}	∫ `x`²³√1+2`x` `dx`
derivative of (x-2^2)	`ddx` ((`x`−2)²)
2(sqrt(xy)-y)dx-xdy=0	2(√`xy`−`y`)`dx`−`xdy`=0
integral of 1/(x^{1/2)}	∫ 1`x`¹² `dx`
integral of x*ln(5+x)	∫ `x`· ln(5+`x`)`dx`
integral of pi/2-5x^{-0.5}	∫ π2 −5`x`^−0.5`dx`
(d^3)/(dx^3)(x^4-8x^3)	`d`³`dx`³ (`x`⁴−8`x`³)
derivative of e^{cos(sqrt(x+3)})	`ddx` (`e`^cos(√x+3))
-8t^2y^{''}-4t(t-4)y^'+4(t-4)y=0	−8`t`²`y`^{′ ′}−4`t`(`t`−4)`y`^′+4(`t`−4)`y`=0
面积 y^2=x,x-2y=3	`area` `y`²=`x`,`x`−2`y`=3
derivative of 3x(x^2-x+1(5x-3))	`ddx` (3`x`(`x`²−`x`+1)(5`x`−3))
(dy)/(dt)=-2y,y(0)= 1/10	`dydt` =−2`y`,`y`(0)=110
tangent x^2-8	`tangent` `x`²−8
derivative of sin(2xcos(2x))	`ddx` (sin(2`x`)cos(2`x`))
tangent f(x)=x^3,\at x=6	`tangent` `f`(`x`)=`x`³,at `x`=6
integral of-9x	∫ −9`xdx`
limit as x approaches 2 of sqrt(51-x)-7	lim _{x→ 2}(√51−`x`−7)

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