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Popular Calculus Problems

derivative of x=4t^2-3t+11	derivative\:x=4t^{2}-3t+11
derivative of sin^2(x+sin(x))	\frac{d}{dx}(\sin^{2}(x)+\sin(x))
derivative of 4cos(t)	derivative\:4\cos(t)
area x=4y^2,x=2+2y^2	area\:x=4y^{2},x=2+2y^{2}
(\partial)/(\partial x)(4x^2+xy+3y^2-8)	\frac{\partial\:}{\partial\:x}(4x^{2}+xy+3y^{2}-8)
integral of sin(x)sec^2(cos(x))	\int\:\sin(x)\sec^{2}(\cos(x))dx
tangent of f(x)=2x^2,\at x=5	tangent\:f(x)=2x^{2},\at\:x=5
integral of 7cos^2(x)sin(2x)	\int\:7\cos^{2}(x)\sin(2x)dx
integral of t^2cos(nt)	\int\:t^{2}\cos(nt)dt
integral of (-x)/x	\int\:\frac{-x}{x}dx
limit as s approaches 0 of sk/(s(s/5+1)*(\frac{s){50}+1)}	\lim\:_{s\to\:0}(s\cdot\:\frac{k}{s\cdot\:(\frac{s}{5}+1)\cdot\:(\frac{s}{50}+1)})
(\partial)/(\partial x)(x^3y^5+9x^5y)	\frac{\partial\:}{\partial\:x}(x^{3}y^{5}+9x^{5}y)
integral of 1/9 (4-x^2)	\int\:\frac{1}{9}(4-x^{2})dx
area y=x^3-x^2-6x,x	area\:y=x^{3}-x^{2}-6x,x
(\partial)/(\partial x)(y^5sin(5x))	\frac{\partial\:}{\partial\:x}(y^{5}\sin(5x))
derivative of (2x^4+3x^2-1)/(x^2)	derivative\:\frac{2x^{4}+3x^{2}-1}{x^{2}}
derivative of x^4(x-3^3)	\frac{d}{dx}(x^{4}(x-3)^{3})
integral of 8x^5e^{5x^6}	\int\:8x^{5}e^{5x^{6}}dx
(d^2y)/(dx^2)-2(dy)/(dx)+y=0	\frac{d^{2}y}{dx^{2}}-2\frac{dy}{dx}+y=0
area y=9ln(5x),y=11,[2,4]	area\:y=9\ln(5x),y=11,[2,4]
integral of sin^2(x)	\int\:\sin^{2}(x)dx
derivative of x^{1/4}y^{3/4}	\frac{d}{dx}(x^{\frac{1}{4}}y^{\frac{3}{4}})
derivative of (x^4+7x^2-9)^5	derivative\:(x^{4}+7x^{2}-9)^{5}
integral of ((x+1)/(sqrt(x-1)))	\int\:(\frac{x+1}{\sqrt{x-1}})dx
tangent of f(x)=e^x,\at x=ln(13)	tangent\:f(x)=e^{x},\at\:x=\ln(13)
tangent of f(x)=e^x(8+3x+5x^2),\at x=0	tangent\:f(x)=e^{x}(8+3x+5x^{2}),\at\:x=0
derivative of x^3e^{-4x}	\frac{d}{dx}(x^{3}e^{-4x})
(dy)/(dx)+y-4cos(x)=0	\frac{dy}{dx}+y-4\cos(x)=0
integral from 0 to 5 of 1/(x^{17/18)}	\int\:_{0}^{5}\frac{1}{x^{\frac{17}{18}}}dx
integral of ve^{uv}	\int\:ve^{uv}du
derivative of f(x)=sqrt((5-2x)(3x-1)^3)	derivative\:f(x)=\sqrt{(5-2x)(3x-1)^{3}}
integral of (x+3)/(3x^2-6x+8)	\int\:\frac{x+3}{3x^{2}-6x+8}dx
(d^2)/(dx^2)(4x\sqrt[3]{x})	\frac{d^{2}}{dx^{2}}(4x\sqrt[3]{x})
d/(dt)((2t)/(4+t^2))	\frac{d}{dt}(\frac{2t}{4+t^{2}})
integral from 1 to 3 of (x^2+2x-4)	\int\:_{1}^{3}(x^{2}+2x-4)dx
sum from n=1 to infinity of (5^n)/(3^n)	\sum\:_{n=1}^{\infty\:}\frac{5^{n}}{3^{n}}
integral of 1/((x^2+y^2)^{3/2)}	\int\:\frac{1}{(x^{2}+y^{2})^{\frac{3}{2}}}dx
3y^{''}-24y^'+36y=6sin(2x)	3y^{\prime\:\prime\:}-24y^{\prime\:}+36y=6\sin(2x)
derivative of 1/(sqrt(1+x^8))	\frac{d}{dx}(\frac{1}{\sqrt{1+x^{8}}})
integral of 6e^{-0.5x}	\int\:6e^{-0.5x}dx
(\partial)/(\partial x)(ln(5x^2-2y^2))	\frac{\partial\:}{\partial\:x}(\ln(5x^{2}-2y^{2}))
integral from 1 to 3 of 2/(4+(x-1)^2)	\int\:_{1}^{3}\frac{2}{4+(x-1)^{2}}dx
y^'=(2y)/x	y^{\prime\:}=\frac{2y}{x}
limit as x approaches 0 of (\|x^2\|)/x	\lim\:_{x\to\:0}(\frac{\left\|x^{2}\right\|}{x})
derivative of 2sec(cos(x)+2tan(2x))	\frac{d}{dx}(2\sec(\cos(x))+2\tan(2x))
limit as x approaches 5 of (x^2+kx-20)/(x-5)	\lim\:_{x\to\:5}(\frac{x^{2}+kx-20}{x-5})
slope ofintercept (1,128),(4,161)	slopeintercept\:(1,128),(4,161)
derivative of ln(-1/x)	\frac{d}{dx}(\ln(-\frac{1}{x}))
y^'=0.0875-(7y)/(2000),y(0)=50	y^{\prime\:}=0.0875-\frac{7y}{2000},y(0)=50
tangent of f(x)=((3x+5))/(1+x),\at x=1	tangent\:f(x)=\frac{(3x+5)}{1+x},\at\:x=1
derivative of 3x^2-6x-8	\frac{d}{dx}(3x^{2}-6x-8)
integral of (e^x)/(x-1)	\int\:\frac{e^{x}}{x-1}dx
limit as x approaches 0 of ln(1-5x)	\lim\:_{x\to\:0}(\ln(1-5x))
xy^{''}-y^'+y^'=0	xy^{\prime\:\prime\:}-y^{\prime\:}+y^{\prime\:}=0
derivative of (1+x-4sqrt(x)/x)	\frac{d}{dx}(\frac{1+x-4\sqrt{x}}{x})
derivative of y=ln(3x^5)	derivative\:y=\ln(3x^{5})
(dy)/(dx)+2y=2e^x	\frac{dy}{dx}+2y=2e^{x}
derivative of x^2sqrt(10x-3)	\frac{d}{dx}(x^{2}\sqrt{10x-3})
3y^{''}+17y^'+10y=0	3y^{\prime\:\prime\:}+17y^{\prime\:}+10y=0
derivative of mx^{m-2}(m-1)	\frac{d}{dx}(mx^{m-2}(m-1))
area y=e^x,y=e^{-3x},x=ln(6)	area\:y=e^{x},y=e^{-3x},x=\ln(6)
(dy)/(dt)=t^2+13t^2y	\frac{dy}{dt}=t^{2}+13t^{2}y
integral of (e^x+xcos(y))	\int\:(e^{x}+x\cos(y))dy
integral from 3 to 6 of x/(x^2+4x+13)	\int\:_{3}^{6}\frac{x}{x^{2}+4x+13}dx
integral of (x^4)/(sqrt(x^{10)-1)}	\int\:\frac{x^{4}}{\sqrt{x^{10}-1}}dx
derivative of f(x)= 7/(sqrt(x-6))	derivative\:f(x)=\frac{7}{\sqrt{x-6}}
roots e^{kx}	roots\:e^{kx}
(\partial)/(\partial x)(2x^2+4y+1)	\frac{\partial\:}{\partial\:x}(2x^{2}+4y+1)
f(x)= 1/2 ln(x)	f(x)=\frac{1}{2}\ln(x)
integral of (3x-x^3+1)/(x^4)	\int\:\frac{3x-x^{3}+1}{x^{4}}dx
limit as x approaches 10 of ln(100-x^2)	\lim\:_{x\to\:10}(\ln(100-x^{2}))
derivative of x^2+1	derivative\:x^{2}+1
limit as x approaches 0-of (sin(2x))/x	\lim\:_{x\to\:0-}(\frac{\sin(2x)}{x})
integral of (x^3-3x^2+5x-3)/(x-1)	\int\:\frac{x^{3}-3x^{2}+5x-3}{x-1}dx
area y=3x-x^2,y=-5x	area\:y=3x-x^{2},y=-5x
tangent of f(x)=sqrt(3x+1),\at x=5	tangent\:f(x)=\sqrt{3x+1},\at\:x=5
derivative of 2e^{6x}	\frac{d}{dx}(2e^{6x})
derivative of f(x)=\sqrt[5]{x^3-3x}	derivative\:f(x)=\sqrt[5]{x^{3}-3x}
integral of xsqrt(1+x^4)	\int\:x\sqrt{1+x^{4}}dx
derivative of sin^2(x-3y)	\frac{d}{dx}(\sin^{2}(x-3y))
integral of e^xsqrt(3-e^x)	\int\:e^{x}\sqrt{3-e^{x}}dx
integral of 3(x-1)y^3e^{y(1-x)}	\int\:3(x-1)y^{3}e^{y(1-x)}dx
integral of+e^{-0.1x}	\int\:+e^{-0.1x}dx
limit as x approaches 1 of ln(x^{1/2})	\lim\:_{x\to\:1}(\ln(x^{\frac{1}{2}}))
inverse oflaplace 1/(s^3+5s)	inverselaplace\:\frac{1}{s^{3}+5s}
inverse oflaplace 1/(1+sa)	inverselaplace\:\frac{1}{1+sa}
derivative of f(x)=8^{(x^2+4x)}	\frac{d}{dx}f(x)=8^{(x^{2}+4x)}
(dy)/(dx)=e^{2x+3y},y(0)=0	\frac{dy}{dx}=e^{2x+3y},y(0)=0
integral from 6 to infinity of xe^{-2x}	\int\:_{6}^{\infty\:}xe^{-2x}dx
integral of-5cos(x)	\int\:-5\cos(x)dx
y^{''}-8y^'+10y=0	y^{\prime\:\prime\:}-8y^{\prime\:}+10y=0
integral of 8sec^2(x)	\int\:8\sec^{2}(x)dx
limit as x approaches 3 of f(x)(g(x))	\lim\:_{x\to\:3}(f(x)(g(x)))
dy=(y-1)^2dx	dy=(y-1)^{2}dx
limit as x approaches 2 of (sqrt(x^2-4x)-2x)/(2x+5)	\lim\:_{x\to\:2}(\frac{\sqrt{x^{2}-4x}-2x}{2x+5})
y^'-y^2+0.5-20y=0	y^{\prime\:}-y^{2}+0.5-20y=0
derivative of f(x)=3x^4-65x^3	derivative\:f(x)=3x^{4}-65x^{3}
x^2dx+2ydy=0	x^{2}dx+2ydy=0
inverse oflaplace s/(s^2+6s+34)	inverselaplace\:\frac{s}{s^{2}+6s+34}
(\partial)/(\partial y)(((x+y))/(x-y))	\frac{\partial\:}{\partial\:y}(\frac{(x+y)}{x-y})

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