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Popular Calculus Problems

limit as x approaches 0 of 2x^x	\lim\:_{x\to\:0}(2x^{x})
derivative of 1/(10x^{9/10)}	derivative\:\frac{1}{10x^{\frac{9}{10}}}
integral of ln(sqrt(x-1))	\int\:\ln(\sqrt{x-1})dx
limit as n approaches infinity of n/(6^n)	\lim\:_{n\to\:\infty\:}(\frac{n}{6^{n}})
derivative of arctan^2(x)	\frac{d}{dx}(\arctan^{2}(x))
integral of y+y^2cos(x)	\int\:y+y^{2}\cos(x)dx
derivative of (8x^2+8+4)/(sqrt(x))	derivative\:\frac{8x^{2}+8+4}{\sqrt{x}}
integral of (x+5)sqrt(10x+x^2)	\int\:(x+5)\sqrt{10x+x^{2}}dx
tangent of f(x)=x+4/x ,(4,5)	tangent\:f(x)=x+\frac{4}{x},(4,5)
(\partial)/(\partial x)(ysin(xy))	\frac{\partial\:}{\partial\:x}(y\sin(xy))
(dy)/(dx)=(9x^2-6)/(x^2)	\frac{dy}{dx}=\frac{9x^{2}-6}{x^{2}}
(\partial)/(\partial y)(xe^y-x^5+y-3)	\frac{\partial\:}{\partial\:y}(xe^{y}-x^{5}+y-3)
derivative of x/(x^2+y^2+1)	\frac{d}{dx}(\frac{x}{x^{2}+y^{2}+1})
(d^2)/(dx^2)(e^{-3x})	\frac{d^{2}}{dx^{2}}(e^{-3x})
integral from 0 to 1 of-8x5^x	\int\:_{0}^{1}-8x5^{x}dx
(\partial)/(\partial y)(e^ycos(x)-y^2)	\frac{\partial\:}{\partial\:y}(e^{y}\cos(x)-y^{2})
integral of cos^8(θ)sin(θ)	\int\:\cos^{8}(θ)\sin(θ)dθ
slope of y-3=5(x-2)y-3=5(x-2)	slope\:y-3=5(x-2)y-3=5(x-2)
(\partial)/(\partial x)(z^2y^2-e^x)	\frac{\partial\:}{\partial\:x}(z^{2}y^{2}-e^{x})
(\partial)/(\partial y)(y/(x^2-y^2))	\frac{\partial\:}{\partial\:y}(\frac{y}{x^{2}-y^{2}})
integral from 1 to infinity of x^{-1}	\int\:_{1}^{\infty\:}x^{-1}dx
tangent of f(x)= 1/(x-2),(1,-1)	tangent\:f(x)=\frac{1}{x-2},(1,-1)
derivative of \sqrt[4]{x}+1/(x^4)	derivative\:\sqrt[4]{x}+\frac{1}{x^{4}}
integral of sin(7x)sin(4x)	\int\:\sin(7x)\sin(4x)dx
(\partial)/(\partial y)(e^{-x^2-y^2})	\frac{\partial\:}{\partial\:y}(e^{-x^{2}-y^{2}})
limit as x approaches 3 of (tan(x-3))/(3e^{x-3)-x}	\lim\:_{x\to\:3}(\frac{\tan(x-3)}{3e^{x-3}-x})
derivative of 1/(x^2+4)	derivative\:\frac{1}{x^{2}+4}
derivative of (tan(x)/(x^2))	\frac{d}{dx}(\frac{\tan(x)}{x^{2}})
tangent of f(x)=(4x)/(x+3),(1,1)	tangent\:f(x)=\frac{4x}{x+3},(1,1)
d/(dθ)(cos(θ)-θsin(θ))	\frac{d}{dθ}(\cos(θ)-θ\sin(θ))
area 9x^2,8x^4-8x^2	area\:9x^{2},8x^{4}-8x^{2}
(dy)/(dx)+2x^2=0	\frac{dy}{dx}+2x^{2}=0
integral of (e^x)/(e^x+6)	\int\:\frac{e^{x}}{e^{x}+6}dx
derivative of xe^{-1/x}	derivative\:xe^{-\frac{1}{x}}
x(e^{y/x}-1)(dy)/(dx)=e^{y/x}(y-x)	x(e^{\frac{y}{x}}-1)\frac{dy}{dx}=e^{\frac{y}{x}}(y-x)
derivative of (e^x/(7x^3))	\frac{d}{dx}(\frac{e^{x}}{7x^{3}})
integral of (sin(x))/(cos(x)-cos^2(x))	\int\:\frac{\sin(x)}{\cos(x)-\cos^{2}(x)}dx
(dy)/(dx)=((1-y))/(1-x)	\frac{dy}{dx}=\frac{(1-y)}{1-x}
integral of 4cos(2θ-5)	\int\:4\cos(2θ-5)dθ
integral of x+ln(x)	\int\:x+\ln(x)dx
limit as x approaches 0+of-x+1	\lim\:_{x\to\:0+}(-x+1)
y^'= y/x+(y/x)^2	y^{\prime\:}=\frac{y}{x}+(\frac{y}{x})^{2}
derivative of \sqrt[3]{t}	derivative\:\sqrt[3]{t}
integral of sqrt(x)-(x-2)	\int\:\sqrt{x}-(x-2)dx
derivative of ln(w)	derivative\:\ln(w)
d/(dt)(acos(t)+t^2sin(t))	\frac{d}{dt}(a\cos(t)+t^{2}\sin(t))
derivative of g(t)=sqrt(3t+\sqrt{5t+9)}	derivative\:g(t)=\sqrt{3t+\sqrt{5t+9}}
(2x+8y)dx+(8x+4y)dy=0	(2x+8y)dx+(8x+4y)dy=0
derivative of f(x)= x/(x^2-5)	derivative\:f(x)=\frac{x}{x^{2}-5}
limit as x approaches-1 of (x^3+1)/(x+1)	\lim\:_{x\to\:-1}(\frac{x^{3}+1}{x+1})
tangent of f(x)= 4/(3x-1),\at x=3	tangent\:f(x)=\frac{4}{3x-1},\at\:x=3
derivative of ln(4x^3+5x^2+2x+5)	derivative\:\ln(4x^{3}+5x^{2}+2x+5)
area y=5-x^2,y=17-7x	area\:y=5-x^{2},y=17-7x
integral of (x+5)/(x^2+16)	\int\:\frac{x+5}{x^{2}+16}dx
derivative of f(x)=((x^2+3))/x	derivative\:f(x)=\frac{(x^{2}+3)}{x}
slope ofintercept (-1,1),(-2,-1)	slopeintercept\:(-1,1),(-2,-1)
derivative of y=x+5	derivative\:y=x+5
x((dy)/(dx))-y=x^2sin(x)	x(\frac{dy}{dx})-y=x^{2}\sin(x)
sqrt(y)dx+(x-1)dy=0,y(2)=9	\sqrt{y}dx+(x-1)dy=0,y(2)=9
derivative of y=(x^2+8x+3)/(sqrt(x))	derivative\:y=\frac{x^{2}+8x+3}{\sqrt{x}}
derivative of ({g}(x(sqrt(x)))/(ax^2+x))	\frac{d}{dx}(\frac{{g}(x)(\sqrt{x})}{ax^{2}+x})
tangent of 7/(x^2+3)	tangent\:\frac{7}{x^{2}+3}
derivative of x^2sin(x+2xcos(x))	\frac{d}{dx}(x^{2}\sin(x)+2x\cos(x))
(dy)/(dx)=(2y)/(2x+1),y(0)=e	\frac{dy}{dx}=\frac{2y}{2x+1},y(0)=e
integral from 0 to 4 of xe^{x^2}	\int\:_{0}^{4}xe^{x^{2}}dx
integral from 0 to a of xsqrt(x^2+a^2)	\int\:_{0}^{a}x\sqrt{x^{2}+a^{2}}dx
derivative of sin(2(x))	\frac{d}{dx}(\sin(2)(x))
derivative of-y/(x+e^y)	derivative\:-\frac{y}{x+e^{y}}
integral from 0 to 3 of (6t)/((t-4)^2)	\int\:_{0}^{3}\frac{6t}{(t-4)^{2}}dt
integral of (2xe^x)/((x+1)^2)	\int\:\frac{2xe^{x}}{(x+1)^{2}}dx
(\partial)/(\partial x)(y-x^2ye^{-y})	\frac{\partial\:}{\partial\:x}(y-x^{2}ye^{-y})
taylor sin(x^2),0	taylor\:\sin(x^{2}),0
y^{''}+y^'-2y=sin(x)	y^{\prime\:\prime\:}+y^{\prime\:}-2y=\sin(x)
(dy)/(dx)-y=e^{2x}y^3	\frac{dy}{dx}-y=e^{2x}y^{3}
(d^2y)/(dx^2)+y=x^2+2	\frac{d^{2}y}{dx^{2}}+y=x^{2}+2
integral of 1/((t+4)(t-1))	\int\:\frac{1}{(t+4)(t-1)}dt
(xy-y^2)dx-x^2dy=0	(xy-y^{2})dx-x^{2}dy=0
(\partial)/(\partial x)(-5y^2sin(xy^2))	\frac{\partial\:}{\partial\:x}(-5y^{2}\sin(xy^{2}))
(\partial)/(\partial y)(20(y-x^2))	\frac{\partial\:}{\partial\:y}(20(y-x^{2}))
limit as x approaches 1 of (x^2+1)/(x+5)	\lim\:_{x\to\:1}(\frac{x^{2}+1}{x+5})
(x+y)^2dx+(2xy+x^2-6)dy=0,y(1)=1	(x+y)^{2}dx+(2xy+x^{2}-6)dy=0,y(1)=1
derivative of (-6/x)	\frac{d}{dx}(\frac{-6}{x})
(d^2)/(dx^2)((3x+5)/(x^2-x))	\frac{d^{2}}{dx^{2}}(\frac{3x+5}{x^{2}-x})
integral of ln(3x+9)	\int\:\ln(3x+9)dx
integral of (sin(x))/(cos^2(x)+cos(x)-2)	\int\:\frac{\sin(x)}{\cos^{2}(x)+\cos(x)-2}dx
inverse oflaplace (s^2-3)/(s+1*s+2)	inverselaplace\:\frac{s^{2}-3}{s+1\cdot\:s+2}
limit as x approaches 0 of x^5e^{-x^4}	\lim\:_{x\to\:0}(x^{5}e^{-x^{4}})
(\partial)/(\partial x)(e^{-8t}cos(pix))	\frac{\partial\:}{\partial\:x}(e^{-8t}\cos(πx))
area-x+5,x^2	area\:-x+5,x^{2}
3ydx+(x-xy)dy=0	3ydx+(x-xy)dy=0
integral of-0.01(1024pi)^2cos(1024pi)x	\int\:-0.01(1024π)^{2}\cos(1024π)xdx
integral of-cos^2(x)	\int\:-\cos^{2}(x)dx
integral of (1-cos(x))/x	\int\:\frac{1-\cos(x)}{x}dx
(\partial)/(\partial x)((x^2-1)(y+2))	\frac{\partial\:}{\partial\:x}((x^{2}-1)(y+2))
integral of x-(e^x)/(y^2)-2y	\int\:x-\frac{e^{x}}{y^{2}}-2ydy
taylor x^{11/2},1.2	taylor\:x^{\frac{11}{2}},1.2
integral of 1/(1-8x)	\int\:\frac{1}{1-8x}dx
tangent of f(x)=(9x)/((x+1)^2),(0,0)	tangent\:f(x)=\frac{9x}{(x+1)^{2}},(0,0)
derivative of xln(x+2y)	\frac{d}{dx}(x\ln(x+2y))
d/(dt)(t^3-t)	\frac{d}{dt}(t^{3}-t)

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