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Problemas populares de Cálculo

xy^'-y+1=0	xy^{\prime\:}-y+1=0
integral de sqrt(x^2+5x)	\int\:\sqrt{x^{2}+5x}dx
(dy)/(dx)+(3x)/(x^2+1)y=(6x)/(x^2+1)	\frac{dy}{dx}+\frac{3x}{x^{2}+1}y=\frac{6x}{x^{2}+1}
derivada de (e^x/2)	\frac{d}{dx}(\frac{e^{x}}{2})
integral de sin(e^x)e^{2x}	\int\:\sin(e^{x})e^{2x}dx
inversalaplace 3/((s+1)^4)	inverselaplace\:\frac{3}{(s+1)^{4}}
límite cuando x tiende a 1 de 4	\lim\:_{x\to\:1}(4)
(dx)/(dt)+5t^3x^5+x/t =0	\frac{dx}{dt}+5t^{3}x^{5}+\frac{x}{t}=0
derivada de (2-x^2(4x^2+9x)^4)	\frac{d}{dx}((2-x^{2})(4x^{2}+9x)^{4})
derivada de (5^x/(x^5))	\frac{d}{dx}(\frac{5^{x}}{x^{5}})
integral de (x^4+x^2+x)	\int\:(x^{4}+x^{2}+x)dx
(\partial)/(\partial x)(x^8)	\frac{\partial\:}{\partial\:x}(x^{8})
tangent y= 1/(2+3x),(2, 1/8)	tangent\:y=\frac{1}{2+3x},(2,\frac{1}{8})
derivada de 4/(x^2+1)	\frac{d}{dx}(\frac{4}{x^{2}+1})
límite cuando x tiende a 0 de 1/(2x)-1/(e^{2x)-1}	\lim\:_{x\to\:0}(\frac{1}{2x}-\frac{1}{e^{2x}-1})
(\partial)/(\partial x)(x^2)	\frac{\partial\:}{\partial\:x}(x^{2})
derivative sqrt(7x)-sqrt(2x)	derivative\:\sqrt{7x}-\sqrt{2x}
derivative y=20x^3(x^4+5)^4	derivative\:y=20x^{3}(x^{4}+5)^{4}
integral de 0 a 4 de (x-4)^2	\int\:_{0}^{4}(x-4)^{2}dx
(\partial)/(\partial x)(-sin(y))	\frac{\partial\:}{\partial\:x}(-\sin(y))
límite cuando x tiende a 1-de ln(x)	\lim\:_{x\to\:1-}(\ln(x))
(xdy)/(dx)+2y=3	\frac{xdy}{dx}+2y=3
y^{''}+3y^'=2t^4+t^2e^{-3t}+sin(3t)	y^{\prime\:\prime\:}+3y^{\prime\:}=2t^{4}+t^{2}e^{-3t}+\sin(3t)
y^'=xy^2+2xy	y^{\prime\:}=xy^{2}+2xy
serie de n=1 a infinity de 1/(n^{2/3)}	\sum\:_{n=1}^{\infty\:}\frac{1}{n^{\frac{2}{3}}}
integral de 6^{(x-2)}	\int\:6^{(x-2)}dx
integral de 1/(sqrt(5-x^2-4x))	\int\:\frac{1}{\sqrt{5-x^{2}-4x}}dx
x^3(dy)/(dx)=y^2+1	x^{3}\frac{dy}{dx}=y^{2}+1
integral de (12)/((x^2-6x+13)^2)	\int\:\frac{12}{(x^{2}-6x+13)^{2}}dx
integral de (x^2-9)^3(2x)	\int\:(x^{2}-9)^{3}(2x)dx
tangent y=8sqrt(x),(16,32)	tangent\:y=8\sqrt{x},(16,32)
(\partial)/(\partial x)(x+1/x)	\frac{\partial\:}{\partial\:x}(x+\frac{1}{x})
(\partial)/(\partial x)((x-1)^2*(y+4)^2)	\frac{\partial\:}{\partial\:x}((x-1)^{2}\cdot\:(y+4)^{2})
y^{''}+4y^'+4y=e^{-2t}	y^{\prime\:\prime\:}+4y^{\prime\:}+4y=e^{-2t}
derivative f(x)=xsqrt(3-2x^2)	derivative\:f(x)=x\sqrt{3-2x^{2}}
y^'=-y,y(0)=1	y^{\prime\:}=-y,y(0)=1
derivative g(x)=(2x+2)/(x^2+2)	derivative\:g(x)=\frac{2x+2}{x^{2}+2}
serie de n=0 a infinity de n	\sum\:_{n=0}^{\infty\:}n
límite cuando (x,y) tiende a (-6,5) de (x^2cos(piy))/(e^{x+y)}	\lim\:_{(x,y)\to\:(-6,5)}(\frac{x^{2}\cos(πy)}{e^{x+y}})
(d^2)/(dx^2)(cos(pix))	\frac{d^{2}}{dx^{2}}(\cos(πx))
integral de 8/(x^2+9)	\int\:\frac{8}{x^{2}+9}dx
inversalaplace 1/(4s+7)	inverselaplace\:\frac{1}{4s+7}
integral de 12x^2(1-x)	\int\:12x^{2}(1-x)dx
integral de tan^3(θ)sec(θ)	\int\:\tan^{3}(θ)\sec(θ)dθ
(dy)/(dt)+2y=te^{-2t}	\frac{dy}{dt}+2y=te^{-2t}
(\partial)/(\partial x)(-3e^xln(y))	\frac{\partial\:}{\partial\:x}(-3e^{x}\ln(y))
integral de (x^3)/(sqrt(x^2-4))	\int\:\frac{x^{3}}{\sqrt{x^{2}-4}}dx
límite cuando x tiende a 1+de ((2))/(x-1)	\lim\:_{x\to\:1+}(\frac{(2)}{x-1})
integral de-2 a 3 de (x^2-4)	\int\:_{-2}^{3}(x^{2}-4)dx
integral de (2x)/(x^2+6x+13)	\int\:\frac{2x}{x^{2}+6x+13}dx
serie de n=1 a infinity de 1/2 n	\sum\:_{n=1}^{\infty\:}\frac{1}{2}n
integral de sin(7x)cos(5x)	\int\:\sin(7x)\cos(5x)dx
límite cuando h tiende a 0 de (3e^h-3)/h	\lim\:_{h\to\:0}(\frac{3e^{h}-3}{h})
integral de-infinity a 0 de x/(x^4+4)	\int\:_{-\infty\:}^{0}\frac{x}{x^{4}+4}dx
integral de 2/(sqrt(4x^2+4))	\int\:\frac{2}{\sqrt{4x^{2}+4}}dx
integral de ln(3) a ln(5) de e^{2x}	\int\:_{\ln(3)}^{\ln(5)}e^{2x}dx
tangent f(x)=3^x,\at x=0	tangent\:f(x)=3^{x},\at\:x=0
integral de-9sin(3t)	\int\:-9\sin(3t)dt
derivada de (1+\sqrt[3]{x}^3)	\frac{d}{dx}((1+\sqrt[3]{x})^{3})
límite cuando x tiende a 1 de x^{17}-x+3	\lim\:_{x\to\:1}(x^{17}-x+3)
derivada de 3x^2+2y^4	\frac{d}{dx}(3x^{2}+2y^{4})
d/(dy)(e^{-xy})	\frac{d}{dy}(e^{-xy})
integral de (3-x^2)3	\int\:(3-x^{2})3dx
(dy)/(dx)=(1/(sec^2(y)))	\frac{dy}{dx}=(\frac{1}{\sec^{2}(y)})
laplacetransformación sin(t+pi/3)	laplacetransform\:\sin(t+\frac{π}{3})
derivative f(x)=-3	derivative\:f(x)=-3
integral de-2 a 1 de x	\int\:_{-2}^{1}xdx
(dy)/(dx)=e^{2x+5y}	\frac{dy}{dx}=e^{2x+5y}
derivada de (x^2-9x+7/(x^2+9))	\frac{d}{dx}(\frac{x^{2}-9x+7}{x^{2}+9})
derivative 10tan^2(6x)	derivative\:10\tan^{2}(6x)
derivada de 2sin(2x-4sin^9(2x))	\frac{d}{dx}(2\sin(2x)-4\sin^{9}(2x))
derivada de x^{2/3}(5-x)	\frac{d}{dx}(x^{\frac{2}{3}}(5-x))
área 19-x^2,-2x+16,-5,-sqrt(19)	area\:19-x^{2},-2x+16,-5,-\sqrt{19}
(\partial)/(\partial x)(y*sqrt(\|x\|))	\frac{\partial\:}{\partial\:x}(y\cdot\:\sqrt{\left\|x\right\|})
(x^2+1)y^'+9x(y-1)=0,y(0)=2	(x^{2}+1)y^{\prime\:}+9x(y-1)=0,y(0)=2
(dP)/(dt)-aP=b	\frac{dP}{dt}-aP=b
dx+e^{9x}dy=0	dx+e^{9x}dy=0
derivada de-2x-3x^3	\frac{d}{dx}(-2x-3x^{3})
laplacetransformación cos(1/4 t)	laplacetransform\:\cos(\frac{1}{4}t)
integral de (1+3sqrt(x))	\int\:(1+3\sqrt{x})dx
(\partial)/(\partial z)(x-y)	\frac{\partial\:}{\partial\:z}(x-y)
integral de (x+3)/(4x+4)	\int\:\frac{x+3}{4x+4}dx
derivative cos(2/3 x)	derivative\:\cos(\frac{2}{3}x)
integral de sin(x)cos^7(x)	\int\:\sin(x)\cos^{7}(x)dx
derivada de 24sqrt(x)	\frac{d}{dx}(24\sqrt{x})
(\partial)/(\partial x)((xy)/(6x+7y))	\frac{\partial\:}{\partial\:x}(\frac{xy}{6x+7y})
integral de sqrt(x^2+2x-8)	\int\:\sqrt{x^{2}+2x-8}dx
integral de (cos(1/(x^2)))/(x^3)	\int\:\frac{\cos(\frac{1}{x^{2}})}{x^{3}}dx
integral de 0 a 9 de f(x)	\int\:_{0}^{9}f(x)dx
x((dy)/(dx))-(1+x)y=xy^2	x(\frac{dy}{dx})-(1+x)y=xy^{2}
derivative 3e^7	derivative\:3e^{7}
derivada de (1-5x/(1+5x))	\frac{d}{dx}(\frac{1-5x}{1+5x})
(\partial)/(\partial y)(-2ye^{x^2-y^2})	\frac{\partial\:}{\partial\:y}(-2ye^{x^{2}-y^{2}})
integral de (sqrt(1+(9x)/8))	\int\:(\sqrt{1+\frac{9x}{8}})dx
xy^'+y=-2xy^2,y(1)=-2	xy^{\prime\:}+y=-2xy^{2},y(1)=-2
tangent f(x)=x^3+4x^2+5x,\at x=-1	tangent\:f(x)=x^{3}+4x^{2}+5x,\at\:x=-1
integral de 1/(sqrt(4x^2+12x+16))	\int\:\frac{1}{\sqrt{4x^{2}+12x+16}}dx
pendiente (7,-5),(-7,-5)	slope\:(7,-5),(-7,-5)
derivada de y(e^x-1)	\frac{d}{dx}(y(e^{x}-1))
integral de (x/5)^n	\int\:(\frac{x}{5})^{n}dx

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