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Problemas populares de Cálculo

(dx)/(dy)=x(1-x)	\frac{dx}{dy}=x(1-x)
límite cuando x tiende a 0 de (1+x^2)^{1/x}	\lim\:_{x\to\:0}((1+x^{2})^{\frac{1}{x}})
4(d^2x)/(dt^2)+7(dx)/(dt)+15x=0	4\frac{d^{2}x}{dt^{2}}+7\frac{dx}{dt}+15x=0
límite cuando x tiende a 10-de (-8)/(x-10)	\lim\:_{x\to\:10-}(\frac{-8}{x-10})
tangent y=arccos(x)+x	tangent\:y=\arccos(x)+x
derivative 5x^4	derivative\:5x^{4}
(\partial)/(\partial x)(4-x^2+xy-3y^2)	\frac{\partial\:}{\partial\:x}(4-x^{2}+xy-3y^{2})
integral de 2tsin(t)	\int\:2t\sin(t)dt
(\partial)/(\partial x)(y/(x+y))	\frac{\partial\:}{\partial\:x}(\frac{y}{x+y})
tangent f(x)=10-x^2	tangent\:f(x)=10-x^{2}
7x^2(dy)/(dx)=(dy)/(dx)+7xe^{-y}	7x^{2}\frac{dy}{dx}=\frac{dy}{dx}+7xe^{-y}
integral de sin(x/2)*cos(x)	\int\:\sin(\frac{x}{2})\cdot\:\cos(x)dx
derivada de x^2-1/(x^2)	\frac{d}{dx}(x^{2}-\frac{1}{x^{2}})
taylor 1/(x^2),3	taylor\:\frac{1}{x^{2}},3
t^2y^{''}+4ty^'-18y=0	t^{2}y^{\prime\:\prime\:}+4ty^{\prime\:}-18y=0
(\partial)/(\partial x)(-2xe^{-3xy})	\frac{\partial\:}{\partial\:x}(-2xe^{-3xy})
integral de 2x(x^2+15)^7	\int\:2x(x^{2}+15)^{7}dx
derivada de 5+cos(x)	\frac{d}{dx}(5+\cos(x))
y^'+2y=xy^2	y^{\prime\:}+2y=xy^{2}
derivative f(x)=(2x-8)^4(x^2+x+1)^5	derivative\:f(x)=(2x-8)^{4}(x^{2}+x+1)^{5}
área y=x^3-10x^2+21x,y=-x^3+10x^2-21x	area\:y=x^{3}-10x^{2}+21x,y=-x^{3}+10x^{2}-21x
derivative e^{3/x}	derivative\:e^{\frac{3}{x}}
y^{''}-y=(2e^{-x})/((1+e^{-2x))^2}	y^{\prime\:\prime\:}-y=\frac{2e^{-x}}{(1+e^{-2x})^{2}}
(dy)/(dx)+(xy)/(x^2+1)= x/(x^2+1)	\frac{dy}{dx}+\frac{xy}{x^{2}+1}=\frac{x}{x^{2}+1}
límite cuando n tiende a infinity de-3^{-n}	\lim\:_{n\to\:\infty\:}(-3^{-n})
integral de 1/(sqrt(x+1))	\int\:\frac{1}{\sqrt{x+1}}dx
tangent f(x)=8+4x^2-2x^3,\at x=2	tangent\:f(x)=8+4x^{2}-2x^{3},\at\:x=2
x^3y^'=x^2y-y^3	x^{3}y^{\prime\:}=x^{2}y-y^{3}
integral de cos^3(x/(13))	\int\:\cos^{3}(\frac{x}{13})dx
límite cuando x tiende a 0 de x+6	\lim\:_{x\to\:0}(x+6)
derivative y=(9x^4+5x)^3	derivative\:y=(9x^{4}+5x)^{3}
integral de e^{8x+7}	\int\:e^{8x+7}dx
(dx)/(dt)=b(1-x)x	\frac{dx}{dt}=b(1-x)x
(\partial)/(\partial x)(x(x+y)^2)	\frac{\partial\:}{\partial\:x}(x(x+y)^{2})
derivada de (4x^3+9/x)	\frac{d}{dx}(\frac{4x^{3}+9}{x})
d/(dt)(sin(ωt+θ))	\frac{d}{dt}(\sin(ωt+θ))
derivative 3\sqrt[3]{x^5}	derivative\:3\sqrt[3]{x^{5}}
integral de 0 a 1 de (1)	\int\:_{0}^{1}(1)dx
xe^xy^'+2e^xy=0	xe^{x}y^{\prime\:}+2e^{x}y=0
integral de sqrt(9-16x^2)	\int\:\sqrt{9-16x^{2}}dx
integral de (1/(x^2-9))	\int\:(\frac{1}{x^{2}-9})dx
área sqrt(x),-x+6,0	area\:\sqrt{x},-x+6,0
(\partial)/(\partial x)((x^2+9x-4y)^6)	\frac{\partial\:}{\partial\:x}((x^{2}+9x-4y)^{6})
derivada de (2x-1/x)	\frac{d}{dx}(\frac{2x-1}{x})
integral de 1/(-cos(u)+1)	\int\:\frac{1}{-\cos(u)+1}du
(\partial)/(\partial y)((2x-3y)^3)	\frac{\partial\:}{\partial\:y}((2x-3y)^{3})
integral de-csc(x)cot(x)	\int\:-\csc(x)\cot(x)dx
integral de (x^2+1)^{-1/2}	\int\:(x^{2}+1)^{-\frac{1}{2}}dx
derivative (x+6)^2	derivative\:(x+6)^{2}
derivada de 5/(x^5+3/(x^2))	\frac{d}{dx}(\frac{5}{x^{5}}+\frac{3}{x^{2}})
integral de \sqrt[3]{4-5x^2}(-10x)	\int\:\sqrt[3]{4-5x^{2}}(-10x)dx
serie de n=1 a infinity de 9e^{-n}	\sum\:_{n=1}^{\infty\:}9e^{-n}
integral de-1 a 3 de xe^{xy}	\int\:_{-1}^{3}xe^{xy}dy
área-x+4,2x,x	area\:-x+4,2x,x
derivada de e^{tx}	\frac{d}{dx}(e^{tx})
integral de 4 a 9 de sqrt(4x)	\int\:_{4}^{9}\sqrt{4x}dx
(\partial)/(\partial x)(x^2 1/(a^2))	\frac{\partial\:}{\partial\:x}(x^{2}\frac{1}{a^{2}})
integral de (13x^3)/(sqrt(7+x^2))	\int\:\frac{13x^{3}}{\sqrt{7+x^{2}}}dx
integral de (3x^2+4x-4)	\int\:(3x^{2}+4x-4)dx
derivada de csc(6x)	\frac{d}{dx}(\csc(6x))
pendiente 2x^4-10x^2	slope\:2x^{4}-10x^{2}
integral de pi/2 a pi de pisin^2(x)	\int\:_{\frac{π}{2}}^{π}π\sin^{2}(x)dx
tangent f(x)=4x^2+2x+5,\at x=3	tangent\:f(x)=4x^{2}+2x+5,\at\:x=3
t((dy)/(dt))+33y= 1/t	t(\frac{dy}{dt})+33y=\frac{1}{t}
derivada de-4x^2+x+5	\frac{d}{dx}(-4x^{2}+x+5)
límite cuando x tiende a pi-de ln(sin(x))	\lim\:_{x\to\:π-}(\ln(\sin(x)))
derivative f(x)=9xe^x	derivative\:f(x)=9xe^{x}
(\partial)/(\partial x)(6yx^5-12y^2x^2)	\frac{\partial\:}{\partial\:x}(6yx^{5}-12y^{2}x^{2})
integral de (m^3)/((m^2+1)^3)	\int\:\frac{m^{3}}{(m^{2}+1)^{3}}dm
pendiente (-2,5),(2,-7)	slope\:(-2,5),(2,-7)
límite cuando x tiende a 2-de (-2)/(x^2-4)	\lim\:_{x\to\:2-}(\frac{-2}{x^{2}-4})
(\partial)/(\partial y)(x-5y)	\frac{\partial\:}{\partial\:y}(x-5y)
límite cuando x tiende a 2 de 7-3x^2-x^3	\lim\:_{x\to\:2}(7-3x^{2}-x^{3})
derivada de 1/4 e^{2x^2}	\frac{d}{dx}(\frac{1}{4}e^{2x^{2}})
(\partial)/(\partial x)(9y^2-1x^2)	\frac{\partial\:}{\partial\:x}(9y^{2}-1x^{2})
integral de 1/((a+bx)x)	\int\:\frac{1}{(a+bx)x}dx
y^{''}-4y^'+2y=0	y^{\prime\:\prime\:}-4y^{\prime\:}+2y=0
derivative f(x)=(6-sec(x))/(tan(x))	derivative\:f(x)=\frac{6-\sec(x)}{\tan(x)}
derivada de 3csc^2(x)	\frac{d}{dx}(3\csc^{2}(x))
integral de x(1+x)^{1/4}	\int\:x(1+x)^{\frac{1}{4}}dx
derivada de (cos(x)/(sin(x)+cos(x)))	\frac{d}{dx}(\frac{\cos(x)}{\sin(x)+\cos(x)})
derivative f(x)=(e^x)/(x^2+4),x=1	derivative\:f(x)=\frac{e^{x}}{x^{2}+4},x=1
derivative f(x)=(x+1)/(x-2)	derivative\:f(x)=\frac{x+1}{x-2}
integral de 0	\int\:0dx
tangent x^4-3x^3+2x^2-x+1	tangent\:x^{4}-3x^{3}+2x^{2}-x+1
derivative f(x)=x^5cos(2x)	derivative\:f(x)=x^{5}\cos(2x)
integral de-2 a 3 de (x^3-6x)	\int\:_{-2}^{3}(x^{3}-6x)dx
integral de x/(x^2sin^2(ln(x)))	\int\:\frac{x}{x^{2}\sin^{2}(\ln(x))}dx
tangent ((x+5))/((x-5))	tangent\:\frac{(x+5)}{(x-5)}
tangent f(x)=x^2-tan(x),\at x=0	tangent\:f(x)=x^{2}-\tan(x),\at\:x=0
(\partial)/(\partial y)(9e^{yz}cos(xyz))	\frac{\partial\:}{\partial\:y}(9e^{yz}\cos(xyz))
integral de (3sqrt(ln^2(x)+25))/x	\int\:\frac{3\sqrt{\ln^{2}(x)+25}}{x}dx
integral de (2x)/(y^2)	\int\:\frac{2x}{y^{2}}dx
derivative sin(xcos(x))	derivative\:\sin(x\cos(x))
derivada de x^2e^{6x}	\frac{d}{dx}(x^{2}e^{6x})
integral de 3 a 7 de k^2+2k-1	\int\:_{3}^{7}k^{2}+2k-1
derivada de-5e^{4x}	\frac{d}{dx}(-5e^{4x})
integral de cos((sqrt(6))/2 t)	\int\:\cos(\frac{\sqrt{6}}{2}t)dt
inversalaplace 3/(s(s^2+2s+5))	inverselaplace\:\frac{3}{s(s^{2}+2s+5)}
límite cuando x tiende a 1 de+(4/(2x-2))	\lim\:_{x\to\:1}(+(\frac{4}{2x-2}))

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