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Problemas populares de Cálculo

y^'=(3x^7e^{y/x}+x^5y^2)/(x^6y)	y^{\prime\:}=\frac{3x^{7}e^{\frac{y}{x}}+x^{5}y^{2}}{x^{6}y}
límite cuando x tiende a 2 de (x-7)/(x+3)	\lim\:_{x\to\:2}(\frac{x-7}{x+3})
integral de 1 a infinity de 1/(x^3-1)	\int\:_{1}^{\infty\:}\frac{1}{x^{3}-1}dx
integral de ysqrt(x+y^2)	\int\:y\sqrt{x+y^{2}}dx
integral de (3sec(x)-cos(x))^2	\int\:(3\sec(x)-\cos(x))^{2}dx
derivative x^2-4x+39	derivative\:x^{2}-4x+39
integral de 1 a 4 de pi(1/x)^2	\int\:_{1}^{4}π(\frac{1}{x})^{2}dx
y^'=3x^2y	y^{\prime\:}=3x^{2}y
límite cuando x tiende a 0+de (ln(x))/(csc(x))	\lim\:_{x\to\:0+}(\frac{\ln(x)}{\csc(x)})
maclaurin f(x)= 1/((1-x)^2)	maclaurin\:f(x)=\frac{1}{(1-x)^{2}}
límite cuando x tiende a 0+de 2(tan(x))^x	\lim\:_{x\to\:0+}(2(\tan(x))^{x})
(dy)/(dx)=((x^2+y^2))/(2xy)	\frac{dy}{dx}=\frac{(x^{2}+y^{2})}{2xy}
y^{''}-y=(e^x)/(e^x+1)	y^{\prime\:\prime\:}-y=\frac{e^{x}}{e^{x}+1}
derivada de ln((x+1/(sqrt(x-2))))	\frac{d}{dx}(\ln(\frac{x+1}{\sqrt{x-2}}))
integral de 1 a infinity de 5/(x^4)	\int\:_{1}^{\infty\:}\frac{5}{x^{4}}dx
integral de (2-x)	\int\:(2-x)dx
límite cuando x tiende a 0+de x^{1/2}	\lim\:_{x\to\:0+}(x^{\frac{1}{2}})
y^'=((x^3+y^3))/(xy^2)	y^{\prime\:}=\frac{(x^{3}+y^{3})}{xy^{2}}
4y^'+ty=7	4y^{\prime\:}+ty=7
(d^2)/(dx^2)(9-x^2)	\frac{d^{2}}{dx^{2}}(9-x^{2})
integral de-x^4	\int\:-x^{4}dx
derivative (3x+1)/(x^2+2x+2)	derivative\:\frac{3x+1}{x^{2}+2x+2}
límite cuando x tiende a 0 de sqrt(x-2)	\lim\:_{x\to\:0}(\sqrt{x-2})
integral de sin(e^{-x})	\int\:\sin(e^{-x})dx
(\partial)/(\partial x)(2x^2+y^2-5y)	\frac{\partial\:}{\partial\:x}(2x^{2}+y^{2}-5y)
derivative e^{-2x}x^3(-x+2)	derivative\:e^{-2x}x^{3}(-x+2)
integral de t^7e^{-t^8}	\int\:t^{7}e^{-t^{8}}dt
límite cuando x tiende a 2 de x/(2-x)	\lim\:_{x\to\:2}(\frac{x}{2-x})
d/(dt)(1-cos(t))	\frac{d}{dt}(1-\cos(t))
derivada de cos^2(5-x)	\frac{d}{dx}(\cos^{2}(5-x))
(dy)/(dt)+e^ty=-5e^t	\frac{dy}{dt}+e^{t}y=-5e^{t}
integral de x^2ycos(x)+2xysin(x)-y^2e^x	\int\:x^{2}y\cos(x)+2xy\sin(x)-y^{2}e^{x}dx
integral de (1/((25-x^2)^{3/2)})	\int\:(\frac{1}{(25-x^{2})^{\frac{3}{2}}})dx
integral de (5+sqrt(x))/(5-sqrt(x))	\int\:\frac{5+\sqrt{x}}{5-\sqrt{x}}dx
derivative f(x)=(2x^2-5x+3)/(5x-3)	derivative\:f(x)=\frac{2x^{2}-5x+3}{5x-3}
integral de (e^{sqrt(x)}+1)/(sqrt(x))	\int\:\frac{e^{\sqrt{x}}+1}{\sqrt{x}}dx
tangent f(x)= 4/(x+1),\at x=1	tangent\:f(x)=\frac{4}{x+1},\at\:x=1
integral de (65)/((x-1)(x^2+64))	\int\:\frac{65}{(x-1)(x^{2}+64)}dx
límite cuando x tiende a 25 de x-25	\lim\:_{x\to\:25}(x-25)
(x+1)dy=(x+6)dx	(x+1)dy=(x+6)dx
(\partial)/(\partial x)(x^2+x)	\frac{\partial\:}{\partial\:x}(x^{2}+x)
y^{''}-2y^'+y=0,y(0)=2,y^'(0)=6	y^{\prime\:\prime\:}-2y^{\prime\:}+y=0,y(0)=2,y^{\prime\:}(0)=6
área y=x^2,y=x^4	area\:y=x^{2},y=x^{4}
integral de (x+4)/(sqrt(x^2+2x+5))	\int\:\frac{x+4}{\sqrt{x^{2}+2x+5}}dx
derivada de (-x^2-7/((x^2-7)^2))	\frac{d}{dx}(\frac{-x^{2}-7}{(x^{2}-7)^{2}})
límite cuando x tiende a 0+de x^{21x}	\lim\:_{x\to\:0+}(x^{21x})
(\partial)/(\partial y)((3y^2-t^2)/(y^5))	\frac{\partial\:}{\partial\:y}(\frac{3y^{2}-t^{2}}{y^{5}})
derivada de (x^2+1^8)	\frac{d}{dx}((x^{2}+1)^{8})
inversalaplace ((2s+1))/(s(2s+10))	inverselaplace\:\frac{(2s+1)}{s(2s+10)}
integral de 8e^{3x+e^{3x}}	\int\:8e^{3x+e^{3x}}dx
derivada de bcos(x)	\frac{d}{dx}(b\cos(x))
pendiente (2.4)(2.3)	slope\:(2.4)(2.3)
integral de (cos^4(x)-sin^4(x))	\int\:(\cos^{4}(x)-\sin^{4}(x))dx
integral de 6t+4	\int\:6t+4dt
integral de 3 a 6 de t^2ln(2t)	\int\:_{3}^{6}t^{2}\ln(2t)dt
integral de sec^2(x)+2	\int\:\sec^{2}(x)+2dx
(\partial)/(\partial x)(2x^2)	\frac{\partial\:}{\partial\:x}(2x^{2})
(dy)/(dx)=sin(2x)-ycos(x)	\frac{dy}{dx}=\sin(2x)-y\cos(x)
derivada de 3x^4-4x^3-12x^2+1	\frac{d}{dx}(3x^{4}-4x^{3}-12x^{2}+1)
integral de (x^2+4x+10)/(x^3+2x^2+5x)	\int\:\frac{x^{2}+4x+10}{x^{3}+2x^{2}+5x}dx
derivada de ln(sqrt(x(1-x)))	\frac{d}{dx}(\ln(\sqrt{x(1-x)}))
derivative ln(X^{1/2})	derivative\:\ln(X^{\frac{1}{2}})
integral de 6/((x+1)^2)	\int\:\frac{6}{(x+1)^{2}}dx
límite cuando x tiende a-3 de (3-x)/(x+3)	\lim\:_{x\to\:-3}(\frac{3-x}{x+3})
inversalaplace (s^2-4s+4)/(s^2-4)	inverselaplace\:\frac{s^{2}-4s+4}{s^{2}-4}
(\partial)/(\partial y)(2sec^2(2x+3y))	\frac{\partial\:}{\partial\:y}(2\sec^{2}(2x+3y))
integral de sqrt(4-9x^2)	\int\:\sqrt{4-9x^{2}}dx
derivative e^{x-y}	derivative\:e^{x-y}
derivative y=7	derivative\:y=7
integral de x^2(x^3+1)^{1/2}	\int\:x^{2}(x^{3}+1)^{\frac{1}{2}}dx
derivative c^{1/2}	derivative\:c^{\frac{1}{2}}
pendiente (-2)/x-(-4)/y =1	slope\:\frac{-2}{x}-\frac{-4}{y}=1
área y=3cos(3x),y=3-3cos(3x),0<= x<= pi/3	area\:y=3\cos(3x),y=3-3\cos(3x),0\le\:x\le\:\frac{π}{3}
derivada de e^{x^3+4x}	\frac{d}{dx}(e^{x^{3}+4x})
integral de (sqrt(x^2-361))/x	\int\:\frac{\sqrt{x^{2}-361}}{x}dx
integral de 0 a 2 de sqrt(36x+145)	\int\:_{0}^{2}\sqrt{36x+145}dx
laplacetransformación t^2+6t-17	laplacetransform\:t^{2}+6t-17
(\partial)/(\partial x)(-x/((x+y)^2))	\frac{\partial\:}{\partial\:x}(-\frac{x}{(x+y)^{2}})
integral de 0 a+oo de x*(x+1)^{-2}	\int\:_{0}^{+oo}x\cdot\:(x+1)^{-2}dx
f(x)=5-x	f(x)=5-x
integral de 0 a 3 de sqrt(1+x)	\int\:_{0}^{3}\sqrt{1+x}dx
derivada de 3/(5x)	\frac{d}{dx}(\frac{3}{5x})
d/(dt)(sqrt(2)sin(t)+sqrt(2))	\frac{d}{dt}(\sqrt{2}\sin(t)+\sqrt{2})
derivada de e^{0.2x}	\frac{d}{dx}(e^{0.2x})
integral de x^4-2x^3+2	\int\:x^{4}-2x^{3}+2dx
integral de 16x^3cos(2-x^4)	\int\:16x^{3}\cos(2-x^{4})dx
d/(du)(cos(u))	\frac{d}{du}(\cos(u))
y^{''}+2y^'+y=0,y(0)=4,y^'(0)=-3	y^{\prime\:\prime\:}+2y^{\prime\:}+y=0,y(0)=4,y^{\prime\:}(0)=-3
derivada de (x^2-3x+1/(x^2))	\frac{d}{dx}(\frac{x^{2}-3x+1}{x^{2}})
límite cuando x tiende a-1 de 8x^4-3x^3+7x	\lim\:_{x\to\:-1}(8x^{4}-3x^{3}+7x)
derivada de sin(x^2+2x-1)	\frac{d}{dx}(\sin(x^{2}+2x-1))
(\partial)/(\partial x)(ln(x+y))	\frac{\partial\:}{\partial\:x}(\ln(x+y))
f(u)=u^2	f(u)=u^{2}
derivative 1/(3+x)	derivative\:\frac{1}{3+x}
derivative x/(x^2-1)	derivative\:\frac{x}{x^{2}-1}
integral de 6e^{3x}-8/(e^{2x)}	\int\:6e^{3x}-\frac{8}{e^{2x}}dx
y^{''}-4y^'+4y=(x+1)e^{2x}	y^{\prime\:\prime\:}-4y^{\prime\:}+4y=(x+1)e^{2x}
tangent f(x)= 1/(sqrt(8x)),\at (x=9)	tangent\:f(x)=\frac{1}{\sqrt{8x}},\at\:(x=9)
serie de n=0 a infinity de (2^n)/((2n)!)x^{2n}	\sum\:_{n=0}^{\infty\:}\frac{2^{n}}{(2n)!}x^{2n}
límite cuando x tiende a 7-de (x-7)/(\|x-7\|)	\lim\:_{x\to\:7-}(\frac{x-7}{\left\|x-7\right\|})

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