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Problemas populares de Cálculo

y^{''}+4y^'+3y=0,y(0)=2,y^'(0)=-1	y^{\prime\:\prime\:}+4y^{\prime\:}+3y=0,y(0)=2,y^{\prime\:}(0)=-1
d/(dθ)(cos^3(θ))	\frac{d}{dθ}(\cos^{3}(θ))
2sqrt(y)dy= 5/(sqrt(x))dx	2\sqrt{y}dy=\frac{5}{\sqrt{x}}dx
derivada de (sqrt(x)+1/(sqrt(x)+3))	\frac{d}{dx}(\frac{\sqrt{x}+1}{\sqrt{x}+3})
(\partial)/(\partial x)(2/3 y^{-1/3})	\frac{\partial\:}{\partial\:x}(\frac{2}{3}y^{-\frac{1}{3}})
y^'=(x+y-1)^2,y(0)=0	y^{\prime\:}=(x+y-1)^{2},y(0)=0
y^{''}-3y^'-4y=e^{4t}	y^{\prime\:\prime\:}-3y^{\prime\:}-4y=e^{4t}
integral de (x,pix)	\int\:(x,πx)dx
derivada de (4(-x^2-4)/((x^2-4)^2))	\frac{d}{dx}(\frac{4(-x^{2}-4)}{(x^{2}-4)^{2}})
(x^2sin(x^2))^'	(x^{2}\sin(x^{2}))^{\prime\:}
integral de ((4x^3-6x^4))/(2x^6)	\int\:\frac{(4x^{3}-6x^{4})}{2x^{6}}dx
tangent f(x)=2x^4+3x-3,(2,35)	tangent\:f(x)=2x^{4}+3x-3,(2,35)
derivative 9a^2+8a-56	derivative\:9a^{2}+8a-56
serie de t=0 a infinity de 1/(t^{0.51)}	\sum\:_{t=0}^{\infty\:}\frac{1}{t^{0.51}}
f(x)=(x/(\sqrt[4]{2x+1)})^{1/x}	f(x)=(\frac{x}{\sqrt[4]{2x+1}})^{\frac{1}{x}}
derivada de tan(10x)	\frac{d}{dx}(\tan(10x))
integral de-3x^2-6x+45	\int\:-3x^{2}-6x+45dx
tangent f(x)= 1/(x^4),\at x=1	tangent\:f(x)=\frac{1}{x^{4}},\at\:x=1
integral de (6x^5+2x)/(x^6+x^2)	\int\:\frac{6x^{5}+2x}{x^{6}+x^{2}}dx
derivada de x^{4/9}	\frac{d}{dx}(x^{\frac{4}{9}})
integral de 6 a 8 de (32)/((x-6)^3)	\int\:_{6}^{8}\frac{32}{(x-6)^{3}}dx
derivative (2x)/(x-3)	derivative\:\frac{2x}{x-3}
y^'+y=e^xy^2	y^{\prime\:}+y=e^{x}y^{2}
integral de 1 a 2 de ((2x+1)(x-2))/x	\int\:_{1}^{2}\frac{(2x+1)(x-2)}{x}dx
derivative f(x)= x/(x-7)	derivative\:f(x)=\frac{x}{x-7}
y^{''}+3y^'+2y= 1/(7+e^x)	y^{\prime\:\prime\:}+3y^{\prime\:}+2y=\frac{1}{7+e^{x}}
derivada de 1+1/(2x)	\frac{d}{dx}(1+\frac{1}{2x})
derivative y=(sqrt(x)-5)/(sqrt(x)+5)	derivative\:y=\frac{\sqrt{x}-5}{\sqrt{x}+5}
x^2y^'+xy=6	x^{2}y^{\prime\:}+xy=6
derivada de (2x+1^2sqrt(3(2x+1)+10))	\frac{d}{dx}((2x+1)^{2}\sqrt{3(2x+1)+10})
inversalaplace 1/(s^2-s+1)	inverselaplace\:\frac{1}{s^{2}-s+1}
serie de n=0 a infinity de 7(2/3)^n	\sum\:_{n=0}^{\infty\:}7(\frac{2}{3})^{n}
integral de (x^3+1)^2x	\int\:(x^{3}+1)^{2}xdx
límite cuando x tiende a 3 de (x+3)/(x+2)	\lim\:_{x\to\:3}(\frac{x+3}{x+2})
derivada de 7/(8x^5)	\frac{d}{dx}(\frac{7}{8x^{5}})
(\partial)/(\partial y)(ycos(z))	\frac{\partial\:}{\partial\:y}(y\cos(z))
integral de e^{3x}cos(3x)	\int\:e^{3x}\cos(3x)dx
(\partial)/(\partial y)(z^2)	\frac{\partial\:}{\partial\:y}(z^{2})
límite cuando x tiende a pi/5 de cot(5x)	\lim\:_{x\to\:\frac{π}{5}}(\cot(5x))
(\partial)/(\partial x)(xy-x+y)	\frac{\partial\:}{\partial\:x}(xy-x+y)
integral de (sqrt(x^2-16))/(x^2)	\int\:\frac{\sqrt{x^{2}-16}}{x^{2}}dx
área 0,x^2,-x+5	area\:0,x^{2},-x+5
integral de 1/(cos(x-1))	\int\:\frac{1}{\cos(x-1)}dx
derivative f(x)=x^3-2x	derivative\:f(x)=x^{3}-2x
límite cuando x tiende a 2 de [6f(x)+g(x)]	\lim\:_{x\to\:2}([6f(x)+g(x)])
área 4x+10,x^2+6x+6,-2,2	area\:4x+10,x^{2}+6x+6,-2,2
(x^2+16)(dy)/(dx)+xy=5x	(x^{2}+16)\frac{dy}{dx}+xy=5x
derivative log_{8}(5x^3+3x)	derivative\:\log_{8}(5x^{3}+3x)
derivative (8x^2+8x+8)/(sqrt(x))	derivative\:\frac{8x^{2}+8x+8}{\sqrt{x}}
taylor x 9/6 ,7	taylor\:x\frac{9}{6},7
integral de 0 a 2 de (1+x^2)	\int\:_{0}^{2}(1+x^{2})dx
(\partial)/(\partial x)((x^2)/(16-y^2))	\frac{\partial\:}{\partial\:x}(\frac{x^{2}}{16-y^{2}})
implicit y',x^2-y^2=9	implicit\:y\prime\:,x^{2}-y^{2}=9
derivada de 3cos(2x+sin(2x)+4)	\frac{d}{dx}(3\cos(2x)+\sin(2x)+4)
pendiente (5, 1/2),(495/62 ,3)	slope\:(5,\frac{1}{2}),(\frac{495}{62},3)
integral de 1/(tan(5x))	\int\:\frac{1}{\tan(5x)}dx
integral de (x^2-10x+24)ln(x)	\int\:(x^{2}-10x+24)\ln(x)dx
tangent f(x)= 1/(2+3x),(1, 1/5)	tangent\:f(x)=\frac{1}{2+3x},(1,\frac{1}{5})
laplacetransformación e^{-2t}t	laplacetransform\:e^{-2t}t
taylor e^x,-4	taylor\:e^{x},-4
(\partial)/(\partial y)((2x+3y)^{10})	\frac{\partial\:}{\partial\:y}((2x+3y)^{10})
derivative (1-3t)/(4+t)	derivative\:\frac{1-3t}{4+t}
integral de 1/(7x+1)	\int\:\frac{1}{7x+1}dx
tangent y= 2/x ,(4, 1/2)	tangent\:y=\frac{2}{x},(4,\frac{1}{2})
tangent f(x)=e^{-x}ln(x),(1,0)	tangent\:f(x)=e^{-x}\ln(x),(1,0)
integral de 1/(x(x^2+4)^2)	\int\:\frac{1}{x(x^{2}+4)^{2}}dx
d/(dθ)(2sin(5θ))	\frac{d}{dθ}(2\sin(5θ))
derivative 6^{x^3}	derivative\:6^{x^{3}}
integral de 1 a 10 de x/(x^2-4)	\int\:_{1}^{10}\frac{x}{x^{2}-4}dx
derivative g(x)=2^{x^2+1x}	derivative\:g(x)=2^{x^{2}+1x}
(\partial)/(\partial x)(x^2tan(4x^4y))	\frac{\partial\:}{\partial\:x}(x^{2}\tan(4x^{4}y))
derivada de x^2sin^3(5x)	\frac{d}{dx}(x^{2}\sin^{3}(5x))
integral de 1/(x^2sqrt(x^2-64))	\int\:\frac{1}{x^{2}\sqrt{x^{2}-64}}dx
integral de 1/(sqrt(t^2-8t+25))	\int\:\frac{1}{\sqrt{t^{2}-8t+25}}dt
integral de e^{2x+5}	\int\:e^{2x+5}dx
(dy)/(dx)=(2x)/(y^2)	\frac{dy}{dx}=\frac{2x}{y^{2}}
integral de (13)/((x-3)(x^2+4))	\int\:\frac{13}{(x-3)(x^{2}+4)}dx
f(x)=(2ln(x))/x	f(x)=\frac{2\ln(x)}{x}
integral de sqrt(e^{18x)-4}	\int\:\sqrt{e^{18x}-4}dx
límite cuando x tiende a 2 de 6*a+x	\lim\:_{x\to\:2}(6\cdot\:a+x)
inversalaplace ((18))/(s(s^2+6s+18))	inverselaplace\:\frac{(18)}{s(s^{2}+6s+18)}
3xy^'+y=12x	3xy^{\prime\:}+y=12x
integral de (2x)/(x^2)	\int\:\frac{2x}{x^{2}}dx
(\partial)/(\partial y)(5x^2y^3)	\frac{\partial\:}{\partial\:y}(5x^{2}y^{3})
integral de e^x(e^x-1)	\int\:e^{x}(e^{x}-1)dx
derivative 4x^2-5x+2	derivative\:4x^{2}-5x+2
(\partial)/(\partial x)(cos(2x-3y^2))	\frac{\partial\:}{\partial\:x}(\cos(2x-3y^{2}))
integral de (-8x+162)/(x^2+9)	\int\:\frac{-8x+162}{x^{2}+9}dx
x(dy)/(dx)=x^2+2x-3	x\frac{dy}{dx}=x^{2}+2x-3
integral de 0 a 4 de 2pi(4-x)(16-x^2)	\int\:_{0}^{4}2π(4-x)(16-x^{2})dx
derivada de (sin(3xcos(2x))/3)	\frac{d}{dx}(\frac{\sin(3x)\cos(2x)}{3})
integral de e^xe^{e^x}	\int\:e^{x}e^{e^{x}}dx
serie de n=2 a infinity de 1/(n^2+6n+8)	\sum\:_{n=2}^{\infty\:}\frac{1}{n^{2}+6n+8}
taylor-(3x-4)^3,3	taylor\:-(3x-4)^{3},3
integral de 0 a (3pi)/2 de 5\|sin(x)\|	\int\:_{0}^{\frac{3π}{2}}5\left\|\sin(x)\right\|dx
derivative (x^2)/(2+sqrt(x))	derivative\:\frac{x^{2}}{2+\sqrt{x}}
integral de-1 a 64 de 1/(x^{1/3)}	\int\:_{-1}^{64}\frac{1}{x^{\frac{1}{3}}}dx
serie de n=1 a infinity de 2/(3^n)	\sum\:_{n=1}^{\infty\:}\frac{2}{3^{n}}
límite cuando x tiende a 2 de 3+2x+x^2	\lim\:_{x\to\:2}(3+2x+x^{2})
límite cuando x tiende a 3 de (\|x-3\|)/(x+3)	\lim\:_{x\to\:3}(\frac{\left\|x-3\right\|}{x+3})

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