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Popular Calculus Problems

derivative of f(t)=2t^3-3t^2-4t	derivative\:f(t)=2t^{3}-3t^{2}-4t
(\partial)/(\partial x)((4pi^2x)/(y^2))	\frac{\partial\:}{\partial\:x}(\frac{4π^{2}x}{y^{2}})
derivative of 9xe^xcsc(x)	derivative\:9xe^{x}\csc(x)
area 1/x ,1,2	area\:\frac{1}{x},1,2
integral of ((x^2+1))/((x-3)(x-2)^2)	\int\:\frac{(x^{2}+1)}{(x-3)(x-2)^{2}}dx
implicit (dy)/(dx),xy^3+10y^{11}=9	implicit\:\frac{dy}{dx},xy^{3}+10y^{11}=9
area y^2-3x=1,x-y=3	area\:y^{2}-3x=1,x-y=3
(dy)/(dt)=-100y+101cos(t)+99sin(t)	\frac{dy}{dt}=-100y+101\cos(t)+99\sin(t)
tangent of y=2e^x-3x+1,\at x=0	tangent\:y=2e^{x}-3x+1,\at\:x=0
derivative of 4x^2-12x+5	derivative\:4x^{2}-12x+5
integral of-2x^2sin(pix)	\int\:-2x^{2}\sin(πx)dx
integral of y/y	\int\:\frac{y}{y}dy
tangent of f(x)=-1-2cos(x),\at x=-pi/4	tangent\:f(x)=-1-2\cos(x),\at\:x=-\frac{π}{4}
y^'=(x-3)(y+1)^{2/3},y(0)=-1	y^{\prime\:}=(x-3)(y+1)^{\frac{2}{3}},y(0)=-1
derivative of (2x+3/(3x^2-4))	\frac{d}{dx}(\frac{2x+3}{3x^{2}-4})
tangent of (5x-4)^4,\at x=2	tangent\:(5x-4)^{4},\at\:x=2
integral from 0 to 1 of e^{-x}	\int\:_{0}^{1}e^{-x}dx
integral of 2xsqrt(x^2+3)	\int\:2x\sqrt{x^{2}+3}dx
integral of 2sin(x	\int\:2\sin(d)xdx
d/(dt)(\sqrt[7]{t}+6sqrt(t^7))	\frac{d}{dt}(\sqrt[7]{t}+6\sqrt{t^{7}})
integral of 1/((2x-1)(x+3))	\int\:\frac{1}{(2x-1)(x+3)}dx
(\partial)/(\partial x)(3sin(3x))	\frac{\partial\:}{\partial\:x}(3\sin(3x))
integral of sin^6(x/2)	\int\:\sin^{6}(\frac{x}{2})dx
(dy)/(dx)-3y=6	\frac{dy}{dx}-3y=6
slope of f(t)=16t^2	slope\:f(t)=16t^{2}
integral of ln(21x)	\int\:\ln(21x)dx
integral of pi/(20)sin(5x)cos(8x)	\int\:\frac{π}{20}\sin(5x)\cos(8x)dx
integral of 3tsin^2(t)	\int\:3t\sin^{2}(t)dt
tangent of 3x^2,\at x=-1	tangent\:3x^{2},\at\:x=-1
derivative of y=ln(x-3)	derivative\:y=\ln(x-3)
integral of 7cos(x)cos^5(sin(x))	\int\:7\cos(x)\cos^{5}(\sin(x))dx
derivative of sqrt(9x+8)	\frac{d}{dx}(\sqrt{9x+8})
integral of (tan(x))/(sec(x)+4cos(x))	\int\:\frac{\tan(x)}{\sec(x)+4\cos(x)}dx
integral of 12x+5	\int\:12x+5dx
(\partial)/(\partial x)(cos(4y^2-2x))	\frac{\partial\:}{\partial\:x}(\cos(4y^{2}-2x))
derivative of sin(x^{tan(x}))	\frac{d}{dx}(\sin(x^{\tan(x)}))
(2x+1)y^'+2y=4x,y(0)=1	(2x+1)y^{\prime\:}+2y=4x,y(0)=1
(\partial)/(\partial z)(ln(x^2+y^4)-z)	\frac{\partial\:}{\partial\:z}(\ln(x^{2}+y^{4})-z)
25y^{''}-y=xe^{x/5},y(0)=1,y^'(0)=0	25y^{\prime\:\prime\:}-y=xe^{\frac{x}{5}},y(0)=1,y^{\prime\:}(0)=0
limit as x approaches infinity of 1/(x(ln(x))^4)	\lim\:_{x\to\:\infty\:}(\frac{1}{x(\ln(x))^{4}})
integral from 1 to 3 of sqrt(1+(x^3-1/(4x^3))^2)	\int\:_{1}^{3}\sqrt{1+(x^{3}-\frac{1}{4x^{3}})^{2}}dx
(\partial)/(\partial v)(sqrt(uv))	\frac{\partial\:}{\partial\:v}(\sqrt{uv})
(\partial)/(\partial z)(2x^4yz^3)	\frac{\partial\:}{\partial\:z}(2x^{4}yz^{3})
derivative of 3/(4x^8)	\frac{d}{dx}(\frac{3}{4x^{8}})
xy^'+y=6xy^2,y(1)=-4	xy^{\prime\:}+y=6xy^{2},y(1)=-4
derivative of 1-2sin^3(x)	derivative\:1-2\sin^{3}(x)
integral of (x^3)/(e^x)	\int\:\frac{x^{3}}{e^{x}}dx
derivative of (4x^5+6/(x^3))	\frac{d}{dx}(\frac{4x^{5}+6}{x^{3}})
derivative of-5/x	derivative\:-\frac{5}{x}
area x,x^2,[0,1]	area\:x,x^{2},[0,1]
limit as x approaches infinity of x*3	\lim\:_{x\to\:\infty\:}(x\cdot\:3)
tangent of sqrt(x)+sqrt(y)=5	tangent\:\sqrt{x}+\sqrt{y}=5
integral of 2sin(x)-cos(x)	\int\:2\sin(x)-\cos(x)dx
(\partial)/(\partial x)((x^2)/(2y)+(3y^2)/(x^2))	\frac{\partial\:}{\partial\:x}(\frac{x^{2}}{2y}+\frac{3y^{2}}{x^{2}})
d/(dy)(ysqrt(x^2+y^2))	\frac{d}{dy}(y\sqrt{x^{2}+y^{2}})
sum from k=0 to infinity of (x^k)/(k!)	\sum\:_{k=0}^{\infty\:}\frac{x^{k}}{k!}
area-cos(x),cos^2(x),[(-pi)/2 , pi/2 ]	area\:-\cos(x),\cos^{2}(x),[\frac{-π}{2},\frac{π}{2}]
integral of 12x	\int\:12xdx
integral of 3/t	\int\:\frac{3}{t}dt
limit as x approaches 8 of x/(ln(9-x))	\lim\:_{x\to\:8}(\frac{x}{\ln(9-x)})
limit as x approaches 5 of 2/(x+5)	\lim\:_{x\to\:5}(\frac{2}{x+5})
2(dy)/(dx)=2x-y	2\frac{dy}{dx}=2x-y
(\partial)/(\partial x)(x(sin(xy)))	\frac{\partial\:}{\partial\:x}(x(\sin(xy)))
integral of x^{100}	\int\:x^{100}dx
derivative of y=cos(5x)	derivative\:y=\cos(5x)
integral of 5/(9+4x^2)	\int\:\frac{5}{9+4x^{2}}dx
integral from-infinity to-1 of e^{-22t}	\int\:_{-\infty\:}^{-1}e^{-22t}dt
tangent of f(x)=(12)/(x^2-4),(4,4)	tangent\:f(x)=\frac{12}{x^{2}-4},(4,4)
integral of 7y	\int\:7ydy
derivative of (2x*sqrt(3x-1))/(5x)	derivative\:\frac{2x\cdot\:\sqrt{3x-1}}{5x}
integral of (e^x)/(e^{2x)+16}	\int\:\frac{e^{x}}{e^{2x}+16}dx
integral of (x^3)/(\sqrt[9]{x^2+5)}	\int\:\frac{x^{3}}{\sqrt[9]{x^{2}+5}}dx
derivative of x/(\|x\|)	\frac{d}{dx}(\frac{x}{\left\|x\right\|})
(\partial)/(\partial x)(pi)	\frac{\partial\:}{\partial\:x}(π)
-x(dy)/(dx)+y=0	-x\frac{dy}{dx}+y=0
(d^2)/(dx^2)(sin(x^2))	\frac{d^{2}}{dx^{2}}(\sin(x^{2}))
integral of 24x^2+16x	\int\:24x^{2}+16xdx
d/(d{x)}(({z})/(({x)^2+{y}^2+{z}^2)^{3/2}})	\frac{d}{d{x}}(\frac{{z}}{({x}^{2}+{y}^{2}+{z}^{2})^{\frac{3}{2}}})
inverse oflaplace 1/((s+1)(s+2)^2)	inverselaplace\:\frac{1}{(s+1)(s+2)^{2}}
derivative of 1/(3-2x)	derivative\:\frac{1}{3-2x}
integral of 1/((x^2-4)^{1/2)}	\int\:\frac{1}{(x^{2}-4)^{\frac{1}{2}}}dx
(1+e^x)yy^'=e^x,y(0)=1	(1+e^{x})yy^{\prime\:}=e^{x},y(0)=1
derivative of f(x)=3x^2-8x-sqrt(x)	derivative\:f(x)=3x^{2}-8x-\sqrt{x}
limit as x approaches-3 of x^3-4x^2-7	\lim\:_{x\to\:-3}(x^{3}-4x^{2}-7)
sum from n=1 to infinity of (n-9)/(n+9)	\sum\:_{n=1}^{\infty\:}\frac{n-9}{n+9}
inverse oflaplace ((11s^2-2s+5))/((s-2)(2s-1)(s+1))	inverselaplace\:\frac{(11s^{2}-2s+5)}{(s-2)(2s-1)(s+1)}
laplacetransform-3t	laplacetransform\:-3t
derivative of (2x^5+3x/(x^4))	\frac{d}{dx}(\frac{2x^{5}+3x}{x^{4}})
integral of (5x^4)	\int\:(5x^{4})dx
integral of 3sqrt(x)+1/(sqrt(x))	\int\:3\sqrt{x}+\frac{1}{\sqrt{x}}dx
(df)/(ds)=12s+(5s)/(sqrt(9-s^2))	\frac{df}{ds}=12s+\frac{5s}{\sqrt{9-s^{2}}}
limit as x approaches 0 of x^n	\lim\:_{x\to\:0}(x^{n})
derivative of y=x^3cos(x)	derivative\:y=x^{3}\cos(x)
integral from 0 to 2 of ((x+2)/(x-4))	\int\:_{0}^{2}(\frac{x+2}{x-4})dx
integral of e^{7θ}sin(8θ)	\int\:e^{7θ}\sin(8θ)dθ
integral of 4e^{-0.1x}	\int\:4e^{-0.1x}dx
area 3sin(2x),-2pi,pi	area\:3\sin(2x),-2π,π
limit as x approaches 0 of ((3arccos(1/2+x)-3arccos(1/2)))/x	\lim\:_{x\to\:0}(\frac{(3\arccos(\frac{1}{2}+x)-3\arccos(\frac{1}{2}))}{x})
derivative of e^{-x^7}	\frac{d}{dx}(e^{-x^{7}})
(ln(u))^'	(\ln(u))^{\prime\:}

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