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Problemas populares de Cálculo

(dy)/(dt)=t^2	\frac{dy}{dt}=t^{2}
derivative y=(csc(x^2))/(7x-cos^2(x))	derivative\:y=\frac{\csc(x^{2})}{7x-\cos^{2}(x)}
laplacetransformación 2t^2e^t	laplacetransform\:2t^{2}e^{t}
(d^3)/(dx^3)(e^{x^2})	\frac{d^{3}}{dx^{3}}(e^{x^{2}})
integral de x/((1-x^2)^{3/2)}	\int\:\frac{x}{(1-x^{2})^{\frac{3}{2}}}dx
(\partial)/(\partial y)(x/(sqrt(x^2+y^2)))	\frac{\partial\:}{\partial\:y}(\frac{x}{\sqrt{x^{2}+y^{2}}})
integral de 1200 a 1210 de 0.1x	\int\:_{1200}^{1210}0.1xdx
límite cuando x tiende a 0 de x^3*ln(x)	\lim\:_{x\to\:0}(x^{3}\cdot\:\ln(x))
(\partial)/(\partial z)(3)	\frac{\partial\:}{\partial\:z}(3)
derivative sin(sqrt(x^2))	derivative\:\sin(\sqrt{x^{2}})
derivative f(s)=8^{sqrt(2s-1)}	derivative\:f(s)=8^{\sqrt{2s-1}}
límite cuando x tiende a infinity de-5/x	\lim\:_{x\to\:\infty\:}(-\frac{5}{x})
derivada de (x-7/(sqrt(x)-\sqrt{7)})	\frac{d}{dx}(\frac{x-7}{\sqrt{x}-\sqrt{7}})
derivada de {g}(h,x(h(x)))	\frac{d}{dx}({g}(h,x)(h(x)))
integral de 0 a 2 de xe^{4x}	\int\:_{0}^{2}xe^{4x}dx
y^'=y^3,y(0)=1	y^{\prime\:}=y^{3},y(0)=1
(dy)/(dt)+1/2 y=17sin(2t)	\frac{dy}{dt}+\frac{1}{2}y=17\sin(2t)
integral de cos(sqrt(2x))	\int\:\cos(\sqrt{2x})dx
integral de (tan(x))^4	\int\:(\tan(x))^{4}dx
derivada de (x^2-5x+4/(\|x-1\|))	\frac{d}{dx}(\frac{x^{2}-5x+4}{\left\|x-1\right\|})
derivada de x^{1-a}	\frac{d}{dx}(x^{1-a})
(\partial)/(\partial x)(e^{y/x}*y)	\frac{\partial\:}{\partial\:x}(e^{\frac{y}{x}}\cdot\:y)
límite cuando x tiende a 1 de (e^{x-1}-1)/(ln^2(x))	\lim\:_{x\to\:1}(\frac{e^{x-1}-1}{\ln^{2}(x)})
área x^2-4x+3,3+4x-x^2	area\:x^{2}-4x+3,3+4x-x^{2}
integral de-1 a 1 de (x^2-1)	\int\:_{-1}^{1}(x^{2}-1)dx
(\partial)/(\partial z)(sin(x+2y+3z))	\frac{\partial\:}{\partial\:z}(\sin(x+2y+3z))
derivative f(x)=6x^2(x-9)	derivative\:f(x)=6x^{2}(x-9)
(\partial)/(\partial x)(2/(x^3))	\frac{\partial\:}{\partial\:x}(\frac{2}{x^{3}})
integral de (sqrt(4x^2-9))/x	\int\:\frac{\sqrt{4x^{2}-9}}{x}dx
límite cuando x tiende a 2 de (x^2-4)/(2-x)	\lim\:_{x\to\:2}(\frac{x^{2}-4}{2-x})
integral de e^x+9x	\int\:e^{x}+9xdx
derivada de (x-a^2)	\frac{d}{dx}((x-a)^{2})
derivative sin^2(x)	derivative\:\sin^{2}(x)
derivada de sin^2(xcot(5x))	\frac{d}{dx}(\sin^{2}(x)\cot(5x))
inversalaplace (4s-36)/(s^2-8s+15)	inverselaplace\:\frac{4s-36}{s^{2}-8s+15}
pendiente (0.5)(1)	slope\:(0.5)(1)
d/(du)(ln(u))	\frac{d}{du}(\ln(u))
(y^2-2xy)dx+x^2dy=0	(y^{2}-2xy)dx+x^{2}dy=0
derivada de e^{sqrt(x^2-2x)}	\frac{d}{dx}(e^{\sqrt{x^{2}-2x}})
inversalaplace 1/(s^2(s+3))	inverselaplace\:\frac{1}{s^{2}(s+3)}
inversalaplace 1/((s^2+4s+5))	inverselaplace\:\frac{1}{(s^{2}+4s+5)}
serie de n=0 a infinity de 1/(4^n)	\sum\:_{n=0}^{\infty\:}\frac{1}{4^{n}}
derivative f(x)=(\sqrt[3]{x})/(x-6)	derivative\:f(x)=\frac{\sqrt[3]{x}}{x-6}
límite cuando x tiende a 3 de f(x)(x-1)	\lim\:_{x\to\:3}(f(x)(x-1))
(\partial)/(\partial y)(x-y)	\frac{\partial\:}{\partial\:y}(x-y)
límite cuando x tiende a 0 de ((11^x-1))/x	\lim\:_{x\to\:0}(\frac{(11^{x}-1)}{x})
integral de 5/(cos(x)-1)	\int\:\frac{5}{\cos(x)-1}dx
integral de ycos(x/y)	\int\:y\cos(\frac{x}{y})dx
derivative f(x)=2(sin^3(x))	derivative\:f(x)=2(\sin^{3}(x))
integral de (sin(2x))/(14+cos^2(x))	\int\:\frac{\sin(2x)}{14+\cos^{2}(x)}dx
y^'+2/x y=y^2,y(1)=3	y^{\prime\:}+\frac{2}{x}y=y^{2},y(1)=3
derivada de a/(2y)	\frac{d}{dx}(\frac{a}{2y})
t^3y^'+4t^2y=0	t^{3}y^{\prime\:}+4t^{2}y=0
integral de (3sin^3(x))/(cos(x))	\int\:\frac{3\sin^{3}(x)}{\cos(x)}dx
(\partial)/(\partial x)(2x^2+3y^2+z^2)	\frac{\partial\:}{\partial\:x}(2x^{2}+3y^{2}+z^{2})
derivada de (2x+1/(x-3))	\frac{d}{dx}(\frac{2x+1}{x-3})
derivada de sin(ln(3x^2+x))	\frac{d}{dx}(\sin(\ln(3x^{2}+x)))
derivada de-(10/(10-x))	\frac{d}{dx}(-\frac{10}{10-x})
integral de 1/(x*sqrt(1-x^2))	\int\:\frac{1}{x\cdot\:\sqrt{1-x^{2}}}dx
derivada de axe^{2x}	\frac{d}{dx}(axe^{2x})
tangent f(x)=x^3+x^2+(6/x),\at x=1	tangent\:f(x)=x^{3}+x^{2}+(\frac{6}{x}),\at\:x=1
tangent y=(x-4)^2,\at x=5	tangent\:y=(x-4)^{2},\at\:x=5
(dy)/(dt)=-2y+10	\frac{dy}{dt}=-2y+10
integral de x^3(x^4-1)^5	\int\:x^{3}(x^{4}-1)^{5}dx
tangent y=4e^xcos(x),(0,4)	tangent\:y=4e^{x}\cos(x),(0,4)
(\partial)/(\partial x)(xe^y+ln(x)y)	\frac{\partial\:}{\partial\:x}(x\cdot\:e^{y}+\ln(x)\cdot\:y)
derivative v/(v+c/v)	derivative\:\frac{v}{v+\frac{c}{v}}
integral de 0 a 1 de e^{-5x^2}	\int\:_{0}^{1}e^{-5x^{2}}dx
límite cuando x tiende a infinity de e^{1/2-1/(x^2)}-1	\lim\:_{x\to\:\infty\:}(e^{\frac{1}{2}-\frac{1}{x^{2}}}-1)
serie de n=1 a infinity de 1(1/6)^n	\sum\:_{n=1}^{\infty\:}1(\frac{1}{6})^{n}
serie de n=1 a infinity de n^n(x-3)^n	\sum\:_{n=1}^{\infty\:}n^{n}(x-3)^{n}
integral de 0 a pi/2 de (cos(θ))/(sqrt(1+sin(θ)))	\int\:_{0}^{\frac{π}{2}}\frac{\cos(θ)}{\sqrt{1+\sin(θ)}}dθ
serie de n=0 a infinity de 2((-2)/3)^n	\sum\:_{n=0}^{\infty\:}2(\frac{-2}{3})^{n}
(dy)/(dx)=e^{-(x+y)}	\frac{dy}{dx}=e^{-(x+y)}
integral de e^{-x+2}	\int\:e^{-x+2}dx
área y=4(x+1),y=5(x+1),x=5	area\:y=4(x+1),y=5(x+1),x=5
derivative f(x)=9sin(x)cos(x)	derivative\:f(x)=9\sin(x)\cos(x)
integral de sin(x)cos(2x)	\int\:\sin(x)\cos(2x)dx
taylor cos(x^3)	taylor\:\cos(x^{3})
integral de 1 a infinity de 5e^{-5x}	\int\:_{1}^{\infty\:}5e^{-5x}dx
integral de e^{-x^2}	\int\:e^{-x^{2}}dx
integral de ((2z))/(\sqrt[3]{z^2+1)}	\int\:\frac{(2z)}{\sqrt[3]{z^{2}+1}}dz
derivada de e^{x^2-x+1}	\frac{d}{dx}(e^{x^{2}-x+1})
derivada de x^4+4x^3-2x^2-12x	\frac{d}{dx}(x^{4}+4x^{3}-2x^{2}-12x)
derivada de 10^{-2x}	\frac{d}{dx}(10^{-2x})
integral de (x^2)/(sqrt(2x-1))	\int\:\frac{x^{2}}{\sqrt{2x-1}}dx
inversalaplace 8/((9s^2+12s+4)(s))	inverselaplace\:\frac{8}{(9s^{2}+12s+4)(s)}
integral de x*e^{x^2}	\int\:x\cdot\:e^{x^{2}}dx
(d^2x)/(dt^2)+9x=-sin(3t)	\frac{d^{2}x}{dt^{2}}+9x=-\sin(3t)
(\partial}{\partial x}(ln(\frac{2xy)/z))	\frac{\partial\:}{\partial\:x}(\ln(\frac{2xy}{z}))
integral de (5x)/(3x^{1/3)}	\int\:\frac{5x}{3x^{\frac{1}{3}}}dx
integral de-1 a 1 de (\sqrt[3]{t-2})	\int\:_{-1}^{1}(\sqrt[3]{t-2})dt
tangent y=1.1x+e^x,(0,1)	tangent\:y=1.1x+e^{x},(0,1)
volumenabout y=0,y=x^2,y=4x-x^2,[0,2]	volumeabout\:y=0,y=x^{2},y=4x-x^{2},[0,2]
(1+cos(t))y^'=(1+e^{-y})sin(t),y(0)=0	(1+\cos(t))y^{\prime\:}=(1+e^{-y})\sin(t),y(0)=0
derivative (x^2+5)(8-x)	derivative\:(x^{2}+5)(8-x)
integral de (2x)/(1+4x^2)	\int\:\frac{2x}{1+4x^{2}}dx
derivative 6/(x^3)	derivative\:\frac{6}{x^{3}}
integral de (3x^2)/(4sqrt(5-x^3))	\int\:\frac{3x^{2}}{4\sqrt{5-x^{3}}}dx
tangent f(x)=3x^2-3x,\at x=3	tangent\:f(x)=3x^{2}-3x,\at\:x=3

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