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Popular Calculus Problems

derivative of (2x^2+4x/(2+x^2))	\frac{d}{dx}(\frac{2x^{2}+4x}{2+x^{2}})
integral of cos(t)sin(t)	\int\:\cos(t)\sin(t)dt
derivative of (2x^2-5x+5)/(x-2)	derivative\:\frac{2x^{2}-5x+5}{x-2}
derivative of {f}(xsin(x))	\frac{d}{dx}({f}(x)\sin(x))
limit as x approaches 0 of x/(8x^2-x)	\lim\:_{x\to\:0}(\frac{x}{8x^{2}-x})
derivative of (x-a/(1+x))	\frac{d}{dx}(\frac{x-a}{1+x})
derivative of f(x)=2(x)^4	derivative\:f(x)=2(x)^{4}
f(x)=ln(3x+2)	f(x)=\ln(3x+2)
derivative of (24)/(x^2+12)	derivative\:\frac{24}{x^{2}+12}
derivative of xsqrt(3600-x^2)	derivative\:x\sqrt{3600-x^{2}}
laplacetransform 3e^{-2t}+e^{-t}	laplacetransform\:3e^{-2t}+e^{-t}
derivative of ((x^2+3/(x^2-3))^2)	\frac{d}{dx}((\frac{x^{2}+3}{x^{2}-3})^{2})
integral of 1/(sqrt(x)\sqrt{1+x)}	\int\:\frac{1}{\sqrt{x}\sqrt{1+x}}dx
integral of e^{sqrt(3x+9)}	\int\:e^{\sqrt{3x+9}}dx
derivative of e^{-2x^3+2}	\frac{d}{dx}(e^{-2x^{3}+2})
(\partial)/(\partial y)(e^xcos(x+y))	\frac{\partial\:}{\partial\:y}(e^{x}\cos(x+y))
(\partial)/(\partial x)(2/3 (1-x)^{3/2})	\frac{\partial\:}{\partial\:x}(\frac{2}{3}(1-x)^{\frac{3}{2}})
sum from n=0 to infinity of (1/9)^n	\sum\:_{n=0}^{\infty\:}(\frac{1}{9})^{n}
derivative of 1/(\sqrt[3]{x^2)}	derivative\:\frac{1}{\sqrt[3]{x^{2}}}
derivative of sqrt(x)+3/x+sqrt(5)	\frac{d}{dx}(\sqrt{x}+\frac{3}{x}+\sqrt{5})
(\partial)/(\partial x)(tan(x/2))	\frac{\partial\:}{\partial\:x}(\tan(\frac{x}{2}))
y^{'''}+4y^{''}-35y^'-150y=0	y^{\prime\:\prime\:\prime\:}+4y^{\prime\:\prime\:}-35y^{\prime\:}-150y=0
integral of 1/(x^{1/3)(x^{2/3}+4)}	\int\:\frac{1}{x^{\frac{1}{3}}(x^{\frac{2}{3}}+4)}dx
derivative of cos^2(x^2)	\frac{d}{dx}(\cos^{2}(x^{2}))
derivative of (9^x-15^{-x}/x)	\frac{d}{dx}(\frac{9^{x}-15^{-x}}{x})
slope of (6.3)(4.2)	slope\:(6.3)(4.2)
integral of t^2-1	\int\:t^{2}-1dt
integral of 3/5-7/x	\int\:\frac{3}{5}-\frac{7}{x}dx
integral of 1/(x^{1.00001)}	\int\:\frac{1}{x^{1.00001}}dx
limit as x approaches 0 of x/4	\lim\:_{x\to\:0}(\frac{x}{4})
(dy)/(dx)=-3xy	\frac{dy}{dx}=-3xy
derivative of (x^2-2x+1(1-3x^{-5}))	\frac{d}{dx}((x^{2}-2x+1)(1-3x^{-5}))
derivative of (x-2(x+1)(x+2))	\frac{d}{dx}((x-2)(x+1)(x+2))
derivative of F(x)=(7x^6+2x^3)^4	derivative\:F(x)=(7x^{6}+2x^{3})^{4}
(\partial)/(\partial x)(sin^2(x^3e^y))	\frac{\partial\:}{\partial\:x}(\sin^{2}(x^{3}e^{y}))
integral of 1/(81e^{-8x)+e^{8x}}	\int\:\frac{1}{81e^{-8x}+e^{8x}}dx
derivative of cos(sin(sqrt(2x+5)))	\frac{d}{dx}(\cos(\sin(\sqrt{2x+5})))
derivative of (\sqrt[3]{x}+1^5)	\frac{d}{dx}((\sqrt[3]{x}+1)^{5})
derivative of x\sqrt[3]{1+x^2}	\frac{d}{dx}(x\sqrt[3]{1+x^{2}})
derivative of (ax/b)	\frac{d}{dx}(\frac{ax}{b})
integral of 1/(sqrt((4-x^2)^3))	\int\:\frac{1}{\sqrt{(4-x^{2})^{3}}}dx
y-1+xy^'=4x	y-1+xy^{\prime\:}=4x
tangent of-5x^2	tangent\:-5x^{2}
(\partial)/(\partial x)(((x^2))/(y+1))	\frac{\partial\:}{\partial\:x}(\frac{(x^{2})}{y+1})
integral of y/((y^2-1)^{3/2)}	\int\:\frac{y}{(y^{2}-1)^{\frac{3}{2}}}dy
(ln(x+1))^'	(\ln(x+1))^{\prime\:}
area x^2+1,0,1	area\:x^{2}+1,0,1
limit as x approaches infinity of 1.01^x	\lim\:_{x\to\:\infty\:}(1.01^{x})
(x^2-x+1)y^{''}-(x^2+x)y^'+(x+1)y=0	(x^{2}-x+1)y^{\prime\:\prime\:}-(x^{2}+x)y^{\prime\:}+(x+1)y=0
area y=2187sqrt(x),y=81x^2	area\:y=2187\sqrt{x},y=81x^{2}
maclaurin 6sin(x)	maclaurin\:6\sin(x)
(\partial)/(\partial x)(x^3ye^{xy})	\frac{\partial\:}{\partial\:x}(x^{3}ye^{xy})
(\partial)/(\partial x)(x^2-x+2y^2+yz-10)	\frac{\partial\:}{\partial\:x}(x^{2}-x+2y^{2}+yz-10)
(\partial)/(\partial x)(x(y)^{1/2})	\frac{\partial\:}{\partial\:x}(x(y)^{\frac{1}{2}})
derivative of y=(x^5)/(10)+1/(6x^3)	derivative\:y=\frac{x^{5}}{10}+\frac{1}{6x^{3}}
sum from n=1 to infinity of n/((n+1)!)	\sum\:_{n=1}^{\infty\:}\frac{n}{(n+1)!}
d/(dt)(4e^{2t})	\frac{d}{dt}(4e^{2t})
integral of (e^{4x})/(e^{4x)+1}	\int\:\frac{e^{4x}}{e^{4x}+1}dx
derivative of 7e^{-3x}	\frac{d}{dx}(7e^{-3x})
integral of x^{-5/4}	\int\:x^{-\frac{5}{4}}dx
integral of cos^6(x)	\int\:\cos^{6}(x)dx
(x+y/x)dx-dy=0	(x+\frac{y}{x})dx-dy=0
y^'=2y+e^{2x}cos(3x),y(0)=4	y^{\prime\:}=2y+e^{2x}\cos(3x),y(0)=4
derivative of (6x^2+6x+6)/(sqrt(x))	derivative\:\frac{6x^{2}+6x+6}{\sqrt{x}}
integral of sin(4t)	\int\:\sin(4t)dt
integral of sin(x)sin(2x)	\int\:\sin(x)\sin(2x)dx
y^'=4x+y,y(0)=1	y^{\prime\:}=4x+y,y(0)=1
integral from 0 to 6 of sqrt(6x)-(3x-12)	\int\:_{0}^{6}\sqrt{6x}-(3x-12)dx
integral from 0 to infinity of 1/(7+x)	\int\:_{0}^{\infty\:}\frac{1}{7+x}dx
integral of e^2x	\int\:e^{2}xdx
(e^x+e^{-x})y^'=y^2	(e^{x}+e^{-x})y^{\prime\:}=y^{2}
integral of x^{-4}+2x+3	\int\:x^{-4}+2x+3dx
limit as x approaches 0 of (21^x-1)/x	\lim\:_{x\to\:0}(\frac{21^{x}-1}{x})
integral of 1/(2sqrt(x)(1+x))	\int\:\frac{1}{2\sqrt{x}(1+x)}dx
y^'= 2/3 xsqrt(1-9y^2)	y^{\prime\:}=\frac{2}{3}x\sqrt{1-9y^{2}}
tangent of f(x)=x^2+2,\at x=3	tangent\:f(x)=x^{2}+2,\at\:x=3
derivative of 4xarcsin(x)	\frac{d}{dx}(4x\arcsin(x))
derivative of (ln(1)/x)	\frac{d}{dx}(\frac{\ln(1)}{x})
(\partial)/(\partial x)(2e^ysin(-3x)-4y+xy)	\frac{\partial\:}{\partial\:x}(2e^{y}\sin(-3x)-4y+xy)
7(ln(y))y^'-x^3y=0	7(\ln(y))y^{\prime\:}-x^{3}y=0
inverse oflaplace (e^{-2s})/(s(s+1.1))	inverselaplace\:\frac{e^{-2s}}{s(s+1.1)}
integral from 0 to 1 of xsin(pix)	\int\:_{0}^{1}x\sin(πx)dx
derivative of y= x/((e^x))	derivative\:y=\frac{x}{(e^{x})}
(e^{t^2})^'	(e^{t^{2}})^{\prime\:}
tangent of y= 2/(x-8),(10,1)	tangent\:y=\frac{2}{x-8},(10,1)
integral of (2x)/(sqrt(5-x^4))	\int\:\frac{2x}{\sqrt{5-x^{4}}}dx
normal of y=2x-x^2,(2,0)	normal\:y=2x-x^{2},(2,0)
integral from-1 to 1 of x^{-3}	\int\:_{-1}^{1}x^{-3}dx
(\partial)/(\partial x)((e^x-e^y)/(e^{xy)})	\frac{\partial\:}{\partial\:x}(\frac{e^{x}-e^{y}}{e^{xy}})
(\partial)/(\partial u)(2cos(u))	\frac{\partial\:}{\partial\:u}(2\cos(u))
tangent of y=-2x^2-4x+1,(0,1)	tangent\:y=-2x^{2}-4x+1,(0,1)
derivative of x/(sqrt(2x-1))	derivative\:\frac{x}{\sqrt{2x-1}}
(dy)/(dx)=xy+3x+4y+12	\frac{dy}{dx}=xy+3x+4y+12
integral of ln(3x-2)	\int\:\ln(3x-2)dx
integral of x^3+sin(x)	\int\:x^{3}+\sin(x)dx
derivative of (sin(x)/(sqrt(x)))	\frac{d}{dx}(\frac{\sin(x)}{\sqrt{x}})
simplify (2x^2+1)^3*(sqrt(x^2-1))	simplify\:(2x^{2}+1)^{3}\cdot\:(\sqrt{x^{2}-1})
derivative of \sqrt[3]{sin(x^2+3})	\frac{d}{dx}(\sqrt[3]{\sin(x^{2}+3)})
area 2x+4,2-3x,-x	area\:2x+4,2-3x,-x
tangent of f(x)=12(x-(1/x)^4),\at x=2	tangent\:f(x)=12(x-(\frac{1}{x})^{4}),\at\:x=2

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