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常见 微积分 问题
(dy)/(dt)=e^{-2t+3y}
\frac{dy}{dt}=e^{-2t+3y}
斜率 (-2,-6),(1,6)
slope\:(-2,-6),(1,6)
integral of sqrt(xy-y^2)
\int\:\sqrt{xy-y^{2}}dx
(dy)/(dx)=0.2y-0.001y^2
\frac{dy}{dx}=0.2y-0.001y^{2}
derivative y=ln(4t)
derivative\:y=\ln(4t)
tangent y=2x^2-x^4,(1,1)
tangent\:y=2x^{2}-x^{4},(1,1)
(dy)/(dx)=-2x+3y-5
\frac{dy}{dx}=-2x+3y-5
(\partial)/(\partial z)(x+y+z)
\frac{\partial\:}{\partial\:z}(x+y+z)
integral of e^{at}
\int\:e^{at}dt
(\partial)/(\partial x)(1/4 2^xy^3)
\frac{\partial\:}{\partial\:x}(\frac{1}{4}2^{x}y^{3})
integral of 1/(sqrt(16+x^2))
\int\:\frac{1}{\sqrt{16+x^{2}}}dx
(\partial)/(\partial y)(8xy-1/4 (x+y)^4)
\frac{\partial\:}{\partial\:y}(8xy-\frac{1}{4}(x+y)^{4})
limit as x approaches x of sin(x)
\lim\:_{x\to\:x}(\sin(x))
面积 y=x^2,y=9x,y=-1
area\:y=x^{2},y=9x,y=-1
derivative of-xe^{-x}-e^{-x}+1
\frac{d}{dx}(-xe^{-x}-e^{-x}+1)
integral of (4x^3-2x+1)/x
\int\:\frac{4x^{3}-2x+1}{x}dx
tangent y=3x^3-x^2+1,(2,21)
tangent\:y=3x^{3}-x^{2}+1,(2,21)
limit as x approaches infinity of 2x^2+1
\lim\:_{x\to\:\infty\:}(2x^{2}+1)
derivative of e^x+e
\frac{d}{dx}(e^{x}+e)
integral of (sin^2(x))/(cos^3(x))
\int\:\frac{\sin^{2}(x)}{\cos^{3}(x)}dx
面积 y= 26/5-1/x ,y=x
area\:y=\frac{26}{5}-\frac{1}{x},y=x
面积 2x^2,2x+6,-2,-1
area\:2x^{2},2x+6,-2,-1
limit as x approaches infinity of e^{3x}
\lim\:_{x\to\:\infty\:}(e^{3x})
limit as x approaches 8+of 2/(x-8)
\lim\:_{x\to\:8+}(\frac{2}{x-8})
泰勒 (x-1)ln(x-1),2
taylor\:(x-1)\ln(x-1),2
y^{''}+16y=40sin(4t)
y^{\prime\:\prime\:}+16y=40\sin(4t)
(\partial)/(\partial y)(e^x+e^y)
\frac{\partial\:}{\partial\:y}(e^{x}+e^{y})
y^{''}-2y^'-y=0,y(0)=0,y^'(0)=2sqrt(2)
y^{\prime\:\prime\:}-2y^{\prime\:}-y=0,y(0)=0,y^{\prime\:}(0)=2\sqrt{2}
derivative sqrt(1)
derivative\:\sqrt{1}
tangent y=e^{4x},\at x= 1/4 ln(5)
tangent\:y=e^{4x},\at\:x=\frac{1}{4}\ln(5)
derivative of (4+8xcosh(2x))
\frac{d}{dx}((4+8x)\cosh(2x))
laplace变换 5*sin(2*t)
laplacetransform\:5\cdot\:\sin(2\cdot\:t)
derivative of xye^x
\frac{d}{dx}(xye^{x})
derivative of (x^2+2x-5/((x+1)^2))
\frac{d}{dx}(\frac{x^{2}+2x-5}{(x+1)^{2}})
y^{''}+9/t y^'+(15)/(t^2)y=0
y^{\prime\:\prime\:}+\frac{9}{t}y^{\prime\:}+\frac{15}{t^{2}}y=0
sum from n=1 to infinity of (3^n)/(2^n)
\sum\:_{n=1}^{\infty\:}\frac{3^{n}}{2^{n}}
(\partial)/(\partial x)(2x^{0.5}y^{0.5})
\frac{\partial\:}{\partial\:x}(2x^{0.5}y^{0.5})
derivative 3x^2+8x-25
derivative\:3x^{2}+8x-25
integral of 4x^2+3
\int\:4x^{2}+3dx
derivative w(z)=(3z)/(1+2z)
derivative\:w(z)=\frac{3z}{1+2z}
limit as x approaches infinity of-8
\lim\:_{x\to\:\infty\:}(-8)
面积 cos(x),x^2+2,[0,2]
area\:\cos(x),x^{2}+2,[0,2]
integral of e^{-2x^2}
\int\:e^{-2x^{2}}dx
integral of 4x^4e^{-x}
\int\:4x^{4}e^{-x}dx
integral of (x^6-x^3+49)/(x^4+7x^2)
\int\:\frac{x^{6}-x^{3}+49}{x^{4}+7x^{2}}dx
integral of (6sqrt(x))/(x-1)
\int\:\frac{6\sqrt{x}}{x-1}dx
integral from-1 to 5 of-x^2+4x+5
\int\:_{-1}^{5}-x^{2}+4x+5dx
integral of (x^2)/(sqrt(x^6-7))
\int\:\frac{x^{2}}{\sqrt{x^{6}-7}}dx
d/(dy)(2x^3-x^2y)
\frac{d}{dy}(2x^{3}-x^{2}y)
integral of 1/(x^2-12x+35)
\int\:\frac{1}{x^{2}-12x+35}dx
3x^'-5x=12
3x^{\prime\:}-5x=12
(dy)/(dx)= 1/2 x+y-1
\frac{dy}{dx}=\frac{1}{2}x+y-1
y^{''''}+18y^{''}+81y=0
y^{\prime\:\prime\:\prime\:\prime\:}+18y^{\prime\:\prime\:}+81y=0
limit as x approaches 1 of x^2+2
\lim\:_{x\to\:1}(x^{2}+2)
derivative of (2x/((1+x)^2))
\frac{d}{dx}(\frac{2x}{(1+x)^{2}})
integral of (ln(sqrt(3x)))/x
\int\:\frac{\ln(\sqrt{3x})}{x}dx
derivative-(18)/(t^3)+3/(t^2)
derivative\:-\frac{18}{t^{3}}+\frac{3}{t^{2}}
integral of xsqrt(x+2)
\int\:x\sqrt{x+2}dx
integral of (x-1)ln(x)
\int\:(x-1)\ln(x)dx
(\partial)/(\partial x)(-f(r,x)rsin(x)*sin(x))
\frac{\partial\:}{\partial\:x}(-f(r,x)r\sin(x)\cdot\:\sin(x))
derivative f(x)=(-2x^2-2)^3
derivative\:f(x)=(-2x^{2}-2)^{3}
derivative of-e^{-x}cos(x-e^{-x}sin(x))
\frac{d}{dx}(-e^{-x}\cos(x)-e^{-x}\sin(x))
(\partial)/(\partial x)(xe^{xy}+2y)
\frac{\partial\:}{\partial\:x}(xe^{xy}+2y)
integral of e^{1-2t}
\int\:e^{1-2t}dt
integral of sqrt(2-3x)
\int\:\sqrt{2-3x}dx
(\partial)/(\partial x)(4y^8+3y^2x^2)
\frac{\partial\:}{\partial\:x}(4y^{8}+3y^{2}x^{2})
(x^2+y^2)dx=2xydy
(x^{2}+y^{2})dx=2xydy
麦克劳林 ln(1+e^{-x})
maclaurin\:\ln(1+e^{-x})
integral of 1/(x^{2/3)(2+x^{1/3})}
\int\:\frac{1}{x^{\frac{2}{3}}(2+x^{\frac{1}{3}})}dx
integral of sin(sqrt(t))
\int\:\sin(\sqrt{t})dt
derivative of a*x^2+b*x+c
\frac{d}{dx}(a\cdot\:x^{2}+b\cdot\:x+c)
integral of (x^3+x+1)/(1+x^2)
\int\:\frac{x^{3}+x+1}{1+x^{2}}dx
laplace变换 (t)e^{4t}
laplacetransform\:(t)e^{4t}
integral of sin^2(2x)
\int\:\sin^{2}(2x)dx
integral of 1/(sqrt(9x^2-49))
\int\:\frac{1}{\sqrt{9x^{2}-49}}dx
derivative of (x^2-1^3)
\frac{d}{dx}((x^{2}-1)^{3})
derivative 1/(t^2-1)
derivative\:\frac{1}{t^{2}-1}
integral of (7x-1)/(x^2-1)
\int\:\frac{7x-1}{x^{2}-1}dx
derivative f(x)=sqrt(4x+1)
derivative\:f(x)=\sqrt{4x+1}
integral of ((x^3+16))/(x^2+16)
\int\:\frac{(x^{3}+16)}{x^{2}+16}dx
integral of-tan(x)+C
\int\:-\tan(x)+Cdx
integral of x*cos(8x^2+pi)
\int\:x\cdot\:\cos(8x^{2}+π)dx
泰勒 9sqrt(1+x)
taylor\:9\sqrt{1+x}
derivative sin^3(4x)
derivative\:\sin^{3}(4x)
integral of 3x^2(x^3-4)^4
\int\:3x^{2}(x^{3}-4)^{4}dx
derivative of (2x/(e^{4x)})
\frac{d}{dx}(\frac{2x}{e^{4x}})
y^'=x+y
y^{\prime\:}=x+y
y^{''}+y=sin(6t),y(0)=0,y^'(0)=0
y^{\prime\:\prime\:}+y=\sin(6t),y(0)=0,y^{\prime\:}(0)=0
(\partial)/(\partial x)(1+cos^4(x^4))
\frac{\partial\:}{\partial\:x}(1+\cos^{4}(x^{4}))
derivative sin(ln(w))
derivative\:\sin(\ln(w))
(4y+2t-5)dt+(6y+4t-1)dy=0
(4y+2t-5)dt+(6y+4t-1)dy=0
sum from n=0 to infinity of e^{-an}
\sum\:_{n=0}^{\infty\:}e^{-an}
(2dy)/(dx)+6y=3
\frac{2dy}{dx}+6y=3
limit as x approaches infinity of-12
\lim\:_{x\to\:\infty\:}(-12)
derivative of-(4x-3/((2x^2-3x+1)^2))
\frac{d}{dx}(-\frac{4x-3}{(2x^{2}-3x+1)^{2}})
integral from-5 to 5 of sqrt(4+|x|)
\int\:_{-5}^{5}\sqrt{4+\left|x\right|}dx
limit as x approaches 3+of x-1
\lim\:_{x\to\:3+}(x-1)
integral of sin(2x)cos^3(2x)
\int\:\sin(2x)\cos^{3}(2x)dx
limit as x approaches 4 of (2x)/(x-4)
\lim\:_{x\to\:4}(\frac{2x}{x-4})
(\partial)/(\partial x)(sin(xye^{x^2}))
\frac{\partial\:}{\partial\:x}(\sin(xye^{x^{2}}))
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