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Popular Calculus Problems

derivative of xcos(y-ycos(x))	\frac{d}{dx}(x\cos(y)-y\cos(x))
derivative of e^{t^2}	derivative\:e^{t^{2}}
inverse oflaplace ((s-1))/(s(s^2+s+1))	inverselaplace\:\frac{(s-1)}{s(s^{2}+s+1)}
integral of x/((1+x^2)sqrt(1-x^4))	\int\:\frac{x}{(1+x^{2})\sqrt{1-x^{4}}}dx
x(dy)/(dx)=xtan(y/x)+y	x\frac{dy}{dx}=x\tan(\frac{y}{x})+y
derivative of (9x^6+2x^3)^4	derivative\:(9x^{6}+2x^{3})^{4}
tangent of y=6+4x^2-2x^3,\at x=a	tangent\:y=6+4x^{2}-2x^{3},\at\:x=a
d/(dt)(e^{-t}sin(t))	\frac{d}{dt}(e^{-t}\sin(t))
integral of (arcsin(7x))/(sqrt(1-49x^2))	\int\:\frac{\arcsin(7x)}{\sqrt{1-49x^{2}}}dx
derivative of ln(5/(x^2))	derivative\:\ln(\frac{5}{x^{2}})
area x^2y=4,x=2,y=4	area\:x^{2}y=4,x=2,y=4
maclaurin 9cos(-x)	maclaurin\:9\cos(-x)
integral of 1/(x^2+8x)	\int\:\frac{1}{x^{2}+8x}dx
(dy)/(dx)= y/((x+1))+4x^2+4x	\frac{dy}{dx}=\frac{y}{(x+1)}+4x^{2}+4x
(\partial)/(\partial v)(cos(u))	\frac{\partial\:}{\partial\:v}(\cos(u))
(\partial)/(\partial y)(2xy-3x^2)	\frac{\partial\:}{\partial\:y}(2xy-3x^{2})
limit as x approaches 1 of (2x+1)/(x+2)	\lim\:_{x\to\:1}(\frac{2x+1}{x+2})
derivative of (9x^2-3x-10y^{''}+(x^2+x)y^'+(2x-1)y)	\frac{d}{dx}((9x^{2}-3x-10)y^{\prime\:\prime\:}+(x^{2}+x)y^{\prime\:}+(2x-1)y)
(\partial)/(\partial x)(tan(6+2x^2y^3z^2))	\frac{\partial\:}{\partial\:x}(\tan(6+2x^{2}y^{3}z^{2}))
derivative of ln(-ln(1-x))	\frac{d}{dx}(\ln(-\ln(1-x)))
laplacetransform 2((e^{2t}-e^{2t})/2)sin(2t)	laplacetransform\:2(\frac{e^{2t}-e^{2t}}{2})\sin(2t)
(sin(2pix)+2pixcos(2pix))^'	(\sin(2πx)+2πx\cos(2πx))^{\prime\:}
(dy}{dx}=\frac{x-y)/x	\frac{dy}{dx}=\frac{x-y}{x}
(\partial)/(\partial x)(6x(x^2+3y^2-1)^2)	\frac{\partial\:}{\partial\:x}(6x(x^{2}+3y^{2}-1)^{2})
sum from n=1 to infinity of cos(n)	\sum\:_{n=1}^{\infty\:}\cos(n)
limit as x approaches 0 of (cos(x))/x	\lim\:_{x\to\:0}(\frac{\cos(x)}{x})
(\partial)/(\partial x)(x^2-y^2+5xy)	\frac{\partial\:}{\partial\:x}(x^{2}-y^{2}+5xy)
derivative of f(x)=sqrt(2-x)	derivative\:f(x)=\sqrt{2-x}
y^{''}-4y^'+2y=0,y(0)=0,y^'(0)=9	y^{\prime\:\prime\:}-4y^{\prime\:}+2y=0,y(0)=0,y^{\prime\:}(0)=9
limit as x approaches 1-of x/((x-1)^2)	\lim\:_{x\to\:1-}(\frac{x}{(x-1)^{2}})
(dy}{dx}=\frac{3x+2)/y	\frac{dy}{dx}=\frac{3x+2}{y}
integral of 3/(y^2)	\int\:\frac{3}{y^{2}}dy
integral of e^{(-ln(2)(t))/x}	\int\:e^{\frac{-\ln(2)(t)}{x}}dt
integral of (sqrt(x))/(x^2+1)	\int\:\frac{\sqrt{x}}{x^{2}+1}dx
derivative of-4x+2	\frac{d}{dx}(-4x+2)
integral of 4-2y	\int\:4-2ydy
integral from-64 to 125 of 1/(\sqrt[3]{x)}	\int\:_{-64}^{125}\frac{1}{\sqrt[3]{x}}dx
derivative of (e^x/(6x^2))	\frac{d}{dx}(\frac{e^{x}}{6x^{2}})
integral of cos(3x-2)sin(4-5x)	\int\:\cos(3x-2)\sin(4-5x)dx
area sin(x),[ 11/9 pi, 12/8 pi]	area\:\sin(x),[\frac{11}{9}π,\frac{12}{8}π]
integral of tan^3(x)+tan(x)	\int\:\tan^{3}(x)+\tan(x)dx
slope ofintercept (1.1)(2.4)	slopeintercept\:(1.1)(2.4)
integral of (6arcsin(x))/(x^2)	\int\:\frac{6\arcsin(x)}{x^{2}}dx
taylor 1/((7+x)^3)	taylor\:\frac{1}{(7+x)^{3}}
sum from m=1 to infinity of 3*(1/3)	\sum\:_{m=1}^{\infty\:}3\cdot\:(\frac{1}{3})
integral of (x-3)^2sin(x-3)	\int\:(x-3)^{2}\sin(x-3)dx
integral of 8tan(8x)	\int\:8\tan(8x)dx
y^'=((x^2))/y	y^{\prime\:}=\frac{(x^{2})}{y}
integral of (2-1/x)^2	\int\:(2-\frac{1}{x})^{2}dx
integral from 3 to 0 of (-x^3-2x^2+x-1)	\int\:_{3}^{0}(-x^{3}-2x^{2}+x-1)dx
tangent of y=(sqrt(x))/(x+3),(1,0.25)	tangent\:y=\frac{\sqrt{x}}{x+3},(1,0.25)
derivative of 1/((3x^2+x-3^9))	\frac{d}{dx}(\frac{1}{(3x^{2}+x-3)^{9}})
f(x)=x^{x^2}	f(x)=x^{x^{2}}
limit as x approaches 9 of sqrt(25-x)	\lim\:_{x\to\:9}(\sqrt{25-x})
(\partial)/(\partial x)(2xye^{x^2})	\frac{\partial\:}{\partial\:x}(2xye^{x^{2}})
limit as x approaches 1 of (x-2[x])^2	\lim\:_{x\to\:1}((x-2[x])^{2})
y^{''}+4y^'+5y=e^{-x}-5x	y^{\prime\:\prime\:}+4y^{\prime\:}+5y=e^{-x}-5x
tangent of f(x)=3x^2-10x	tangent\:f(x)=3x^{2}-10x
derivative of pix^3	derivative\:πx^{3}
derivative of y=e^{2x}tan(2x)	derivative\:y=e^{2x}\tan(2x)
slope of y=3x^2-x+1	slope\:y=3x^{2}-x+1
x(dy}{dx}+3(y+x^2)=\frac{sin(x))/x	x\frac{dy}{dx}+3(y+x^{2})=\frac{\sin(x)}{x}
integral of ysqrt(1+y^2)	\int\:y\sqrt{1+y^{2}}dy
x^{''}-5x^'+6x=(t^2+t)sin(t)	x^{\prime\:\prime\:}-5x^{\prime\:}+6x=(t^{2}+t)\sin(t)
limit as x approaches-1-of g(x)	\lim\:_{x\to\:-1-}(g(x))
derivative of f(x)= 3/((2x+1)^{5/2)}	derivative\:f(x)=\frac{3}{(2x+1)^{\frac{5}{2}}}
xy^'-y=-x^2+2x+2	xy^{\prime\:}-y=-x^{2}+2x+2
integral of (x^2+1)/(x^2-x)	\int\:\frac{x^{2}+1}{x^{2}-x}dx
(\partial)/(\partial y)(8xln(xy))	\frac{\partial\:}{\partial\:y}(8x\ln(xy))
t^2y^'+ty=5	t^{2}\cdot\:y^{\prime\:}+t\cdot\:y=5
derivative of e^{xln(x})	\frac{d}{dx}(e^{x\ln(x)})
limit as x approaches 0 of (e^x+x)^{m/x}	\lim\:_{x\to\:0}((e^{x}+x)^{\frac{m}{x}})
integral of 7/(sqrt(9-49x^2))	\int\:\frac{7}{\sqrt{9-49x^{2}}}dx
inverse oflaplace {1/(s^4)}	inverselaplace\:\left\{\frac{1}{s^{4}}\right\}
area 2,-5,y=2x^2+12,y=0	area\:2,-5,y=2x^{2}+12,y=0
limit as x approaches infinity of 4+1/x	\lim\:_{x\to\:\infty\:}(4+\frac{1}{x})
(\partial)/(\partial x)(1/(sqrt(3x-2)))	\frac{\partial\:}{\partial\:x}(\frac{1}{\sqrt{3x-2}})
integral of sin(24x)cos(17x)	\int\:\sin(24x)\cos(17x)dx
integral of x-(x^2)/2+c	\int\:x-\frac{x^{2}}{2}+cdx
sum from n=1 to infinity of 1/(n^2+6n+8)	\sum\:_{n=1}^{\infty\:}\frac{1}{n^{2}+6n+8}
limit as x approaches 0 of ((cos(x)))/x	\lim\:_{x\to\:0}(\frac{(\cos(x))}{x})
derivative of 1/(sqrt(1+4x^2))	\frac{d}{dx}(\frac{1}{\sqrt{1+4x^{2}}})
d/(dt)(pit)	\frac{d}{dt}(πt)
limit as x approaches 0 of ((sin(8x)))/x	\lim\:_{x\to\:0}(\frac{(\sin(8x))}{x})
limit as x approaches 2 of 8x^3+1	\lim\:_{x\to\:2}(8x^{3}+1)
derivative of 8e^{8t+5}	derivative\:8e^{8t+5}
integral of 1/(5-8x)	\int\:\frac{1}{5-8x}dx
limit as x approaches 2 of 2x-1	\lim\:_{x\to\:2}(2x-1)
(sqrt(x^2+1))^'	(\sqrt{x^{2}+1})^{\prime\:}
derivative of xy^{-1}	\frac{d}{dx}(xy^{-1})
(\partial)/(\partial x)(3ln((2xy)/(5z)))	\frac{\partial\:}{\partial\:x}(3\ln(\frac{2xy}{5z}))
integral of (cos(t))/(2+sin(t))	\int\:\frac{\cos(t)}{2+\sin(t)}dt
integral of (x*ln(x))	\int\:(x\cdot\:\ln(x))dx
d/(dj)(3i+4j)	\frac{d}{dj}(3i+4j)
derivative of f(x)=sec^2(x)-3	derivative\:f(x)=\sec^{2}(x)-3
integral of (sqrt(4x^2-81))/(x^3)	\int\:\frac{\sqrt{4x^{2}-81}}{x^{3}}dx
derivative of 3/(8(x+1^{5/2)})	\frac{d}{dx}(\frac{3}{8(x+1)^{\frac{5}{2}}})
(sqrt(e^x))^'	(\sqrt{e^{x}})^{\prime\:}
integral of 9/(x(x^4+7))	\int\:\frac{9}{x(x^{4}+7)}dx
integral of 2x^2cos(x^3)	\int\:2x^{2}\cos(x^{3})dx

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