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Popular Calculus Problems

derivative of y-3x	\frac{d}{dx}(y-3x)
derivative of 2x^3+1/(x^2+16x^{7/2}+5)	\frac{d}{dx}(2x^{3}+\frac{1}{x^{2}}+16x^{\frac{7}{2}}+5)
2xy^'+y=6x,y(4)=20	2xy^{\prime\:}+y=6x,y(4)=20
limit as x approaches 6-of (x+9)/(x+6)	\lim\:_{x\to\:6-}(\frac{x+9}{x+6})
x^{''''}=0	x^{\prime\:\prime\:\prime\:\prime\:}=0
limit as x approaches 5 of sqrt(x)	\lim\:_{x\to\:5}(\sqrt{x})
y^{''}-y^'-6y=0,y^'(0)=-6	y^{\prime\:\prime\:}-y^{\prime\:}-6y=0,y^{\prime\:}(0)=-6
integral of (2-x)/(x^2-x+1)	\int\:\frac{2-x}{x^{2}-x+1}dx
integral of 6e^{-0.8x}	\int\:6e^{-0.8x}dx
sum from n=1 to infinity of (pi/4)^n	\sum\:_{n=1}^{\infty\:}(\frac{π}{4})^{n}
derivative of 4x^2-5x+3	\frac{d}{dx}(4x^{2}-5x+3)
integral of sqrt(x)-x^2	\int\:\sqrt{x}-x^{2}dx
derivative of x^3+2x+3	\frac{d}{dx}(x^{3}+2x+3)
derivative of f(x)=4x^2+9x	derivative\:f(x)=4x^{2}+9x
integral from-2 to 1 of sqrt(1+(-3)^2)	\int\:_{-2}^{1}\sqrt{1+(-3)^{2}}dx
integral of cos^2(x)sin^4(x)	\int\:\cos^{2}(x)\sin^{4}(x)dx
integral of e^{-sx}*x^2	\int\:e^{-sx}\cdot\:x^{2}dx
tangent of-x^2+9x+3,\at x=5	tangent\:-x^{2}+9x+3,\at\:x=5
area y=x^2,y=sqrt(x),y=0	area\:y=x^{2},y=\sqrt{x},y=0
sum from n=2 to infinity of e^{3-4n}	\sum\:_{n=2}^{\infty\:}e^{3-4n}
derivative of f(x)=(2x-8)4(x^2+x+1)5	derivative\:f(x)=(2x-8)4(x^{2}+x+1)5
inverse oflaplace (s+2)/(s^2-s-12)	inverselaplace\:\frac{s+2}{s^{2}-s-12}
limit as x approaches 0 of 3x^{7x}	\lim\:_{x\to\:0}(3x^{7x})
integral of (x^2+24x-16)/(x^3-16x)	\int\:\frac{x^{2}+24x-16}{x^{3}-16x}dx
derivative of 6/(7t^4)	derivative\:\frac{6}{7t^{4}}
limit as x approaches-2 of 3/((x+2))	\lim\:_{x\to\:-2}(\frac{3}{(x+2)})
(\partial)/(\partial x)(ycos(xy))	\frac{\partial\:}{\partial\:x}(y\cos(xy))
derivative of [x+(x+sin^2(x))^7]^3	derivative\:[x+(x+\sin^{2}(x))^{7}]^{3}
limit as x approaches 2+of e^{-x}	\lim\:_{x\to\:2+}(e^{-x})
laplacetransform te^{-t}sin(t)	laplacetransform\:te^{-t}\sin(t)
integral of 1/(6-7x)	\int\:\frac{1}{6-7x}dx
integral of 5x[(9-4x^2)^2]^{1/3}	\int\:5x[(9-4x^{2})^{2}]^{\frac{1}{3}}dx
integral from 0 to 0.6 of 300x	\int\:_{0}^{0.6}300xdx
(dy)/(dx)= y/x+8x+7	\frac{dy}{dx}=\frac{y}{x}+8x+7
(\partial)/(\partial x)(8xarctan(x/y))	\frac{\partial\:}{\partial\:x}(8x\arctan(\frac{x}{y}))
derivative of e^{x/(x-1})	\frac{d}{dx}(e^{\frac{x}{x-1}})
integral of (x^3)/(x^2-x)	\int\:\frac{x^{3}}{x^{2}-x}dx
derivative of (1+1/x ^{1/x})	\frac{d}{dx}((1+\frac{1}{x})^{\frac{1}{x}})
(\partial)/(\partial x)(xysqrt(x^2+y^2))	\frac{\partial\:}{\partial\:x}(xy\sqrt{x^{2}+y^{2}})
integral of 3xsin(5x)	\int\:3x\sin(5x)dx
area x=9y^2,x=28+2y^2	area\:x=9y^{2},x=28+2y^{2}
integral of-e^t	\int\:-e^{t}dt
tangent of f(x)=3-6x^2,-57,\at x=3	tangent\:f(x)=3-6x^{2},-57,\at\:x=3
limit as x approaches 3-of ln(x-3)	\lim\:_{x\to\:3-}(\ln(x-3))
(\partial)/(\partial x)(x+sqrt(x)sqrt(y))	\frac{\partial\:}{\partial\:x}(x+\sqrt{x}\sqrt{y})
derivative of (2x^{3/2}-x^2+4/x)	\frac{d}{dx}(\frac{2x^{\frac{3}{2}}-x^{2}+4}{x})
derivative of 1/(x^7+2/(x^3))	\frac{d}{dx}(\frac{1}{x^{7}}+\frac{2}{x^{3}})
integral from-1 to 1 of 2-2x^2	\int\:_{-1}^{1}2-2x^{2}dx
y^{''}+2y^'+y=x^2e^{-x}	y^{\prime\:\prime\:}+2y^{\prime\:}+y=x^{2}e^{-x}
derivative of tan(t)	derivative\:\tan(t)
derivative of f(x)=36x(9-x^2)^{-2}	derivative\:f(x)=36x(9-x^{2})^{-2}
integral from 1 to 4 of 1/(6-sqrt(x))	\int\:_{1}^{4}\frac{1}{6-\sqrt{x}}dx
f(x)=arcsin(x^2)	f(x)=\arcsin(x^{2})
sum from n=1 to infinity of n/(2n)	\sum\:_{n=1}^{\infty\:}\frac{n}{2n}
derivative of f(x)=(x^2-8)(x^2+9)	derivative\:f(x)=(x^{2}-8)(x^{2}+9)
integral of x-3	\int\:x-3dx
integral of ((sin(x)))/x	\int\:\frac{(\sin(x))}{x}dx
integral of-0.2x^2+12x	\int\:-0.2x^{2}+12xdx
integral of sqrt(4x^4+x^2)	\int\:\sqrt{4x^{4}+x^{2}}dx
derivative of f(x)= 4/((3x)^{-2)}	derivative\:f(x)=\frac{4}{(3x)^{-2}}
integral of 5/(x^{-1)+5}	\int\:\frac{5}{x^{-1}+5}dx
limit as x approaches infinity of 1/x-3	\lim\:_{x\to\:\infty\:}(\frac{1}{x}-3)
derivative of (7x^2/(sqrt(x)))	\frac{d}{dx}(\frac{7x^{2}}{\sqrt{x}})
integral from 0 to 1 of 9(x^2+1)e^{-x}	\int\:_{0}^{1}9(x^{2}+1)e^{-x}dx
integral of x/(sqrt(2x+3))	\int\:\frac{x}{\sqrt{2x+3}}dx
integral of x^3e^{9x}	\int\:x^{3}e^{9x}dx
area y=10x^4-10x^2,y=7x^2	area\:y=10x^{4}-10x^{2},y=7x^{2}
sqrt(x)+sqrt(y)*(dy)/(dx)=0	\sqrt{x}+\sqrt{y}\cdot\:\frac{dy}{dx}=0
slope of (0.3)(4.1)	slope\:(0.3)(4.1)
area y=e^x,y=e^{-4x},x=ln(4)	area\:y=e^{x},y=e^{-4x},x=\ln(4)
integral of 1/(x(x+1)(x+2))	\int\:\frac{1}{x(x+1)(x+2)}dx
derivative of e^{(-x/4})	\frac{d}{dx}(e^{\frac{-x}{4}})
(\partial)/(\partial y)(e^{-x}cos(yz)z)	\frac{\partial\:}{\partial\:y}(e^{-x}\cos(yz)z)
(\partial)/(\partial y)(3x-4xy+9y)	\frac{\partial\:}{\partial\:y}(3x-4xy+9y)
derivative of (x-2/(x-1))	\frac{d}{dx}(\frac{x-2}{x-1})
integral from 0 to 1 of 5x-5x^2	\int\:_{0}^{1}5x-5x^{2}dx
inverse oflaplace ((s+1)^2)/(s^2-s-6)	inverselaplace\:\frac{(s+1)^{2}}{s^{2}-s-6}
(\partial)/(\partial x)(sin(6x^3y-6xy^2))	\frac{\partial\:}{\partial\:x}(\sin(6x^{3}y-6xy^{2}))
derivative of 7/(x^8+5x+1)	\frac{d}{dx}(\frac{7}{x^{8}+5x+1})
derivative of sin(14x)	\frac{d}{dx}(\sin(14x))
y^'=1+y^2+x+xy^2	y^{\prime\:}=1+y^{2}+x+xy^{2}
integral of ((1+x))/x	\int\:\frac{(1+x)}{x}dx
limit as x approaches 0 of 2x+12	\lim\:_{x\to\:0}(2x+12)
derivative of ln(sec^2(x))	derivative\:\ln(\sec^{2}(x))
y^{''}+16y=2sec(4x)	y^{\prime\:\prime\:}+16y=2\sec(4x)
limit as x approaches 7 of-x^2+x-7	\lim\:_{x\to\:7}(-x^{2}+x-7)
integral of 1/(T-70)	\int\:\frac{1}{T-70}dT
limit as x approaches 0 of (xsin(1/x))/x	\lim\:_{x\to\:0}(\frac{x\sin(\frac{1}{x})}{x})
derivative of x^3-1/x	\frac{d}{dx}(x^{3}-\frac{1}{x})
limit as x approaches 0 of xcos(x^2)	\lim\:_{x\to\:0}(x\cos(x^{2}))
integral of x*(x^2+1)^2	\int\:x\cdot\:(x^{2}+1)^{2}dx
(\partial)/(\partial x)(x-x^2y)	\frac{\partial\:}{\partial\:x}(x-x^{2}y)
derivative of (sin(2x)/4)	\frac{d}{dx}(\frac{\sin(2x)}{4})
integral from 0 to pi of cos^4(x)sin(x)	\int\:_{0}^{π}\cos^{4}(x)\sin(x)dx
(\partial)/(\partial y)(x+2y-6)	\frac{\partial\:}{\partial\:y}(x+2y-6)
integral from-8 to 8 of 64-x^2	\int\:_{-8}^{8}64-x^{2}dx
integral of 9xe^{x^2}	\int\:9xe^{x^{2}}dx
laplacetransform h(t-2pi)sin(t-2pi)	laplacetransform\:h(t-2π)\sin(t-2π)
derivative of x^4y	\frac{d}{dx}(x^{4}y)
derivative of 1/(x^2y)	\frac{d}{dx}(\frac{1}{x^{2}y})

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