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Popular Calculus Problems

(\partial)/(\partial x)((y-x^2)^2+x^5)	\frac{\partial\:}{\partial\:x}((y-x^{2})^{2}+x^{5})
taylor g(x)= 1/((1+2x)^3)	taylor\:g(x)=\frac{1}{(1+2x)^{3}}
taylor 1-cos(x)	taylor\:1-\cos(x)
integral from-pi to pi of pisin^2(x)	\int\:_{-π}^{π}π\sin^{2}(x)dx
sum from n=1 to infinity}(((-2)^{n-1 of))/(7^n)	\sum\:_{n=1}^{\infty\:}\frac{((-2)^{n-1})}{7^{n}}
integral from 0 to 1 of (-4y)/(e^{2y)}	\int\:_{0}^{1}\frac{-4y}{e^{2y}}dy
(\partial)/(\partial x)(6x^2y+9xy^3)	\frac{\partial\:}{\partial\:x}(6x^{2}y+9xy^{3})
(\partial)/(\partial x)(-xy(12-x-y))	\frac{\partial\:}{\partial\:x}(-xy(12-x-y))
(\partial)/(\partial t)(ln(x+t^2))	\frac{\partial\:}{\partial\:t}(\ln(x+t^{2}))
derivative of (7+8x-4sqrt(x)/x)	\frac{d}{dx}(\frac{7+8x-4\sqrt{x}}{x})
integral of (sqrt(484-x^2))/x	\int\:\frac{\sqrt{484-x^{2}}}{x}dx
area x^3,x+6=y,(-x)/2 =y	area\:x^{3},x+6=y,\frac{-x}{2}=y
(\partial)/(\partial y)(ln(sqrt(xy)))	\frac{\partial\:}{\partial\:y}(\ln(\sqrt{xy}))
integral of (1/(xsqrt(x^2-1)))	\int\:(\frac{1}{x\sqrt{x^{2}-1}})dx
y^{''}+4y^'+5y=-5x+3e^{-x}	y^{\prime\:\prime\:}+4y^{\prime\:}+5y=-5x+3e^{-x}
d/(dθ)(cos(θ)-2sin(θ))	\frac{d}{dθ}(\cos(θ)-2\sin(θ))
limit as x approaches 0-of ax^2+b/2	\lim\:_{x\to\:0-}(ax^{2}+\frac{b}{2})
tangent of 2/(x^2),\at (1.2)	tangent\:\frac{2}{x^{2}},\at\:(1.2)
integral of 1/(xln^4(x))	\int\:\frac{1}{x\ln^{4}(x)}dx
y^'=y^{1/3}	y^{\prime\:}=y^{\frac{1}{3}}
(dy)/(dx)=5x+15y	\frac{dy}{dx}=5x+15y
f(x)= x/(4x+3ln(x))	f(x)=\frac{x}{4x+3\ln(x)}
slope of y=(-4x^2+12)/(2x+2)	slope\:y=\frac{-4x^{2}+12}{2x+2}
derivative of arcsin(e^{-x})	\frac{d}{dx}(\arcsin(e^{-x}))
limit as x approaches-9 of 1-4x^3	\lim\:_{x\to\:-9}(1-4x^{3})
integral from 0 to 5 of 2e^x	\int\:_{0}^{5}2e^{x}dx
limit as x approaches 2 of 3x^3+5x	\lim\:_{x\to\:2}(3x^{3}+5x)
limit as x approaches pi/2 of 4sin(x)	\lim\:_{x\to\:\frac{π}{2}}(4\sin(x))
limit as x approaches 1-of (x+2)/(1-x)	\lim\:_{x\to\:1-}(\frac{x+2}{1-x})
tangent of f(x)=5x^2-2x,\at x=3	tangent\:f(x)=5x^{2}-2x,\at\:x=3
derivative of f(x)= 1/2 x^3-2x+3	derivative\:f(x)=\frac{1}{2}x^{3}-2x+3
integral of (12x^3-24x^2+7)/(x^2-2x)	\int\:\frac{12x^{3}-24x^{2}+7}{x^{2}-2x}dx
derivative of (sqrt(s)-3)/(sqrt(s)+7)	derivative\:\frac{\sqrt{s}-3}{\sqrt{s}+7}
limit as x approaches-2 of (-1)/(-x^2+4)	\lim\:_{x\to\:-2}(\frac{-1}{-x^{2}+4})
(dy)/(dx)=4x+(9x^2)/((3x^3+1)^{3/2)}	\frac{dy}{dx}=4x+\frac{9x^{2}}{(3x^{3}+1)^{\frac{3}{2}}}
integral from 0 to 1 of (3x+1)cos(x)	\int\:_{0}^{1}(3x+1)\cos(x)dx
derivative of-9x^2+4x+5	\frac{d}{dx}(-9x^{2}+4x+5)
integral of cot^4(x)	\int\:\cot^{4}(x)dx
(dy)/(dx)=sqrt(y/x)	\frac{dy}{dx}=\sqrt{\frac{y}{x}}
integral of 1/((pix-1))	\int\:\frac{1}{(πx-1)}dx
integral of 4^{ln(x)}	\int\:4^{\ln(x)}dx
integral of sin(x)x	\int\:\sin(x)xdx
derivative of 2sin(x)+2xcos(x)	derivative\:2\sin(x)+2x\cos(x)
integral of e^ycos(2y)	\int\:e^{y}\cos(2y)dy
limit as x approaches 2 of (2x-25)/(x-2)	\lim\:_{x\to\:2}(\frac{2x-25}{x-2})
integral from-infinity to 0 of 1/(6-10x)	\int\:_{-\infty\:}^{0}\frac{1}{6-10x}dx
area \|9x\|,x^2-10	area\:\left\|9x\right\|,x^{2}-10
integral of q^2cos(7q)	\int\:q^{2}\cos(7q)dq
(dy)/(dx)=((y-y^3))/(a^2),y(0)=b	\frac{dy}{dx}=\frac{(y-y^{3})}{a^{2}},y(0)=b
(\partial)/(\partial x)(bxe^{5xy})	\frac{\partial\:}{\partial\:x}(bxe^{5xy})
limit as x approaches (-1)+of 1/(x+1)	\lim\:_{x\to\:(-1)+}(\frac{1}{x+1})
limit as x approaches 2 of (4/x-2)/(x-2)	\lim\:_{x\to\:2}(\frac{\frac{4}{x}-2}{x-2})
(\partial)/(\partial x)(z^2)	\frac{\partial\:}{\partial\:x}(z^{2})
integral of (5x)/(5x^2+2)	\int\:\frac{5x}{5x^{2}+2}dx
derivative of f(x)=e^6+ln(4)	derivative\:f(x)=e^{6}+\ln(4)
derivative of 4x^3-24x^2+36x	\frac{d}{dx}(4x^{3}-24x^{2}+36x)
(dP)/(dt)=1P(500-P)	\frac{dP}{dt}=1P(500-P)
derivative of-sin(3x)	derivative\:-\sin(3x)
x*y^'+y= 1/(y^2)	x\cdot\:y^{\prime\:}+y=\frac{1}{y^{2}}
integral of 2xsqrt(1+4x^2)	\int\:2x\sqrt{1+4x^{2}}dx
derivative of cos(7^{6x})	\frac{d}{dx}(\cos(7^{6x}))
x^2(dy)/(dx)+xy=1	x^{2}\frac{dy}{dx}+xy=1
integral of sec^2(6x)	\int\:\sec^{2}(6x)dx
integral of t/(e^t)	\int\:\frac{t}{e^{t}}dt
integral of (x+3)/(x^2-x+4)	\int\:\frac{x+3}{x^{2}-x+4}dx
y^{''}+2y^'+y=4e-t	y^{\prime\:\prime\:}+2y^{\prime\:}+y=4e-t
derivative of 1y^2-7y^4(y+9y^3)	derivative\:1y^{2}-7y^{4}(y+9y^{3})
limit as x approaches 36 of (x^2)/9-4/x	\lim\:_{x\to\:36}(\frac{x^{2}}{9}-\frac{4}{x})
integral of 7/(4+7x)	\int\:\frac{7}{4+7x}dx
(\partial)/(\partial x)(3x^2y+xsin(2y))	\frac{\partial\:}{\partial\:x}(3x^{2}y+x\sin(2y))
y^'+sin(t)y=-sin(t),y(0)=7	y^{\prime\:}+\sin(t)y=-\sin(t),y(0)=7
(\partial)/(\partial x)(1/4 x^ay^{1-a})	\frac{\partial\:}{\partial\:x}(\frac{1}{4}x^{a}y^{1-a})
integral of e^{-2}	\int\:e^{-2}dx
area 4x-12,[2,6]	area\:4x-12,[2,6]
integral of e^{2*x}	\int\:e^{2\cdot\:x}dx
derivative of (x^{12}-1)^3	derivative\:(x^{12}-1)^{3}
integral of (7x^3+x^2)/(sqrt(x))	\int\:\frac{7x^{3}+x^{2}}{\sqrt{x}}dx
limit as x approaches infinity of 3^x	\lim\:_{x\to\:\infty\:}(3^{x})
y^'=(y-y^2)/x	y^{\prime\:}=\frac{y-y^{2}}{x}
derivative of x^{2/5}	derivative\:x^{\frac{2}{5}}
tangent of sqrt(9-t)	tangent\:\sqrt{9-t}
(d^2)/(dx^2)((x^2-3x)/(x+1))	\frac{d^{2}}{dx^{2}}(\frac{x^{2}-3x}{x+1})
sum from n=1 to infinity of 6e^{-5n}	\sum\:_{n=1}^{\infty\:}6e^{-5n}
integral of (12x^3-24x^2+5)/(x^2-2x)	\int\:\frac{12x^{3}-24x^{2}+5}{x^{2}-2x}dx
(\partial)/(\partial x)(sqrt(x)+4y)	\frac{\partial\:}{\partial\:x}(\sqrt{x}+4y)
integral of e^{2x}2x	\int\:e^{2x}2xdx
(\partial)/(\partial x)(sqrt(x^2-y))	\frac{\partial\:}{\partial\:x}(\sqrt{x^{2}-y})
derivative of f(x)=x^3arcsin(x^2e^x)	derivative\:f(x)=x^{3}\arcsin(x^{2}e^{x})
inverse oflaplace (s-2)/(s^2+5s+6)	inverselaplace\:\frac{s-2}{s^{2}+5s+6}
derivative of (x^3)/4+1/(3x)	derivative\:\frac{x^{3}}{4}+\frac{1}{3x}
(\partial)/(\partial t)(3t)	\frac{\partial\:}{\partial\:t}(3t)
(dv)/(dt)=-2v-32	\frac{dv}{dt}=-2v-32
y^{''}=-16y	y^{\prime\:\prime\:}=-16y
limit as x approaches 1 of e^{8x^2-8x}	\lim\:_{x\to\:1}(e^{8x^{2}-8x})
derivative of f(x)=(18e^x)/(7^x)	derivative\:f(x)=\frac{18e^{x}}{7^{x}}
integral of tan^3(x)sec^8(x)	\int\:\tan^{3}(x)\sec^{8}(x)dx
derivative of 2/3 x^3	derivative\:\frac{2}{3}x^{3}
limit as x approaches 0+of tan(2/x)	\lim\:_{x\to\:0+}(\tan(\frac{2}{x}))
integral of e^{x^2+4x+3}(x+2)	\int\:e^{x^{2}+4x+3}(x+2)dx
(\partial)/(\partial y)((xy)/((x-y)))	\frac{\partial\:}{\partial\:y}(\frac{xy}{(x-y)})

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