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Problemas populares de Cálculo

derivada de e^xcos(x-e^xsin(x))	\frac{d}{dx}(e^{x}\cos(x)-e^{x}\sin(x))
derivada de (sin(x/4+cos(x))^{1/x})	\frac{d}{dx}((\sin(\frac{x}{4})+\cos(x))^{\frac{1}{x}})
(1x+ye^{y/x})dx-xe^{y/x}dy=0	(1x+ye^{\frac{y}{x}})dx-xe^{\frac{y}{x}}dy=0
límite cuando x tiende a 8+de 3/(x-8)	\lim\:_{x\to\:8+}(\frac{3}{x-8})
integral de ln((7x)^2)	\int\:\ln((7x)^{2})dx
(\partial)/(\partial x)(cos(2x+4y))	\frac{\partial\:}{\partial\:x}(\cos(2x+4y))
derivada de-(x^2/2)	\frac{d}{dx}(-\frac{x^{2}}{2})
3y^'=(3xy+18x^2+2y^2)/(x^2),y(1)=3	3\cdot\:y^{\prime\:}=\frac{3x\cdot\:y+18x^{2}+2y^{2}}{x^{2}},y(1)=3
derivative 2\sqrt[5]{x^3}	derivative\:2\sqrt[5]{x^{3}}
tangent f(x)=(-8x)/(x^2+1),\at x=0	tangent\:f(x)=\frac{-8x}{x^{2}+1},\at\:x=0
integral de 1/x-3/(x^2+1)	\int\:\frac{1}{x}-\frac{3}{x^{2}+1}dx
integral de (2sin(x))	\int\:(2\sin(x))dx
(\partial)/(\partial x)(e^x(x^2-y^2))	\frac{\partial\:}{\partial\:x}(e^{x}(x^{2}-y^{2}))
derivada de x-sqrt(1+x^2)	\frac{d}{dx}(x-\sqrt{1+x^{2}})
derivada de (3x^3/2)	\frac{d}{dx}(\frac{3x^{3}}{2})
derivada de sin(x+x^2)	\frac{d}{dx}(\sin(x)+x^{2})
(\partial)/(\partial y)(xe^{y^2})	\frac{\partial\:}{\partial\:y}(xe^{y^{2}})
(ye^{xy}cos(2x)-2e^{xy}sin(2x)+2x)+(xe^{xy}cos(2x)-3)y^'=0	(ye^{xy}\cos(2x)-2e^{xy}\sin(2x)+2x)+(xe^{xy}\cos(2x)-3)y^{\prime\:}=0
límite cuando x tiende a 0 de (1-6x)^{5/x}	\lim\:_{x\to\:0}((1-6x)^{\frac{5}{x}})
(dy)/(dx)+7y=6	\frac{dy}{dx}+7y=6
serie de n=1 a infinity de 5(7/8)^n	\sum\:_{n=1}^{\infty\:}5(\frac{7}{8})^{n}
derivada de (3sqrt(x)/x)	\frac{d}{dx}(\frac{3\sqrt{x}}{x})
derivative 18t^2-11t+4	derivative\:18t^{2}-11t+4
x^2y^'+4/3 xy=-2cos(4x)y^{-1/2}	x^{2}y^{\prime\:}+\frac{4}{3}xy=-2\cos(4x)y^{-\frac{1}{2}}
integral de 5 a 8 de x/(x^2-2)	\int\:_{5}^{8}\frac{x}{x^{2}-2}dx
derivada de (a+x^2/(a-x^2))	\frac{d}{dx}(\frac{a+x^{2}}{a-x^{2}})
taylor 3xln(1+x)	taylor\:3x\ln(1+x)
integral de x^{1/3}+(2x)^{1/3}	\int\:x^{\frac{1}{3}}+(2x)^{\frac{1}{3}}dx
y^'-2y=e^{2t}	y^{\prime\:}-2y=e^{2t}
área y=13-x^2,y=x^2-5	area\:y=13-x^{2},y=x^{2}-5
(dy)/(dx)-sin(x)y=2sin(x)	\frac{dy}{dx}-\sin(x)y=2\sin(x)
d/(dt)((dx)/(dt))+d/(dt)x+2x=t^3	\frac{d}{dt}(\frac{dx}{dt})+\frac{d}{dt}x+2x=t^{3}
x^2(dy)/(dx)=y-xy,y(-1)=-3	x^{2}\frac{dy}{dx}=y-xy,y(-1)=-3
integral de 1/((e^{-x)+1)}	\int\:\frac{1}{(e^{-x}+1)}dx
integral de (-4x^3-8x^2-4)	\int\:(-4x^{3}-8x^{2}-4)dx
integral de ((x^2+1))/(sqrt(3+2x-x^2))	\int\:\frac{(x^{2}+1)}{\sqrt{3+2x-x^{2}}}dx
derivative g(t)=5(cos(pit))^2	derivative\:g(t)=5(\cos(πt))^{2}
integral de-6sin(3x)	\int\:-6\sin(3x)dx
derivada de e^{2x}x	\frac{d}{dx}(e^{2x}x)
pendienteintercept (2,-4),(6,0)	slopeintercept\:(2,-4),(6,0)
(\partial)/(\partial x)(2xcos(x^2+y^2))	\frac{\partial\:}{\partial\:x}(2x\cos(x^{2}+y^{2}))
límite cuando x tiende a-3+de (x^2-9)/(x+3)	\lim\:_{x\to\:-3+}(\frac{x^{2}-9}{x+3})
xy+y^'=142x	xy+y^{\prime\:}=142x
(dy)/(dx)=2x-1+2xy-y	\frac{dy}{dx}=2x-1+2xy-y
pendiente (-19.7,10.5),(-18.9,3.4)	slope\:(-19.7,10.5),(-18.9,3.4)
derivada de cos(2pix)	\frac{d}{dx}(\cos(2πx))
pendiente (0,-9),(-4,0)	slope\:(0,-9),(-4,0)
inversalaplace t^6e^{8t}	inverselaplace\:t^{6}e^{8t}
f(x)=3e^{2x}	f(x)=3e^{2x}
límite cuando x tiende a 3+de 8-x	\lim\:_{x\to\:3+}(8-x)
derivative f(x)=tan(pix)	derivative\:f(x)=\tan(πx)
tangent sqrt(x+4)	tangent\:\sqrt{x+4}
y'=0.0019y(900-y)	y\prime\:=0.0019y(900-y)
tangent f(x)=x^x,\at x=1	tangent\:f(x)=x^{x},\at\:x=1
(\partial)/(\partial s)(se^t)	\frac{\partial\:}{\partial\:s}(se^{t})
derivada de (x-2^3+1)	\frac{d}{dx}((x-2)^{3}+1)
(\partial)/(\partial x)(3x^3y^2)	\frac{\partial\:}{\partial\:x}(3x^{3}y^{2})
derivative (3x)/(2(1-2x))	derivative\:\frac{3x}{2(1-2x)}
integral de cos(θ/2)	\int\:\cos(\frac{θ}{2})dθ
derivada de x^2sin(x+2xcos(x)-2sin(x))	\frac{d}{dx}(x^{2}\sin(x)+2x\cos(x)-2\sin(x))
integral de 9 a 16 de 1/(9-sqrt(x))	\int\:_{9}^{16}\frac{1}{9-\sqrt{x}}dx
derivada de-(11/((x-3)^2))	\frac{d}{dx}(-\frac{11}{(x-3)^{2}})
(\partial)/(\partial x)(xye^{-x-y})	\frac{\partial\:}{\partial\:x}(xye^{-x-y})
límite cuando x tiende a-3-de (x^2)/(x+3)	\lim\:_{x\to\:-3-}(\frac{x^{2}}{x+3})
derivada de (cot(x+csc(x))^{-1})	\frac{d}{dx}((\cot(x)+\csc(x))^{-1})
integral de 0 a 2 de (2-t)sqrt(t)	\int\:_{0}^{2}(2-t)\sqrt{t}dt
integral de (t^6+1)/(t^6+t^3)	\int\:\frac{t^{6}+1}{t^{6}+t^{3}}dt
integral de 31x^{30}	\int\:31x^{30}dx
integral de (y+4)/(y^2+y)	\int\:\frac{y+4}{y^{2}+y}dy
integral de (e^x)/(e^{2x)-9}	\int\:\frac{e^{x}}{e^{2x}-9}dx
x^2y^'+4xy-e^x=0	x^{2}y^{\prime\:}+4xy-e^{x}=0
derivada de ((x^5-5)/(x+1))	\frac{d}{dx}(\frac{(x^{5}-5)}{x+1})
integral de 1 a 2 de (2x^2-2)	\int\:_{1}^{2}(2x^{2}-2)dx
integral de (x^2+3x-1)e^{2x}	\int\:(x^{2}+3x-1)e^{2x}dx
integral de (sin(2x)*sinh(2x))/2	\int\:\frac{\sin(2x)\cdot\:\sinh(2x)}{2}dx
integral de cos(x)(7+4sin^2(x))	\int\:\cos(x)(7+4\sin^{2}(x))dx
(\partial)/(\partial y)(y^3e^x-4y+1)	\frac{\partial\:}{\partial\:y}(y^{3}e^{x}-4y+1)
integral de sec^2(x)(tan(x)+3)	\int\:\sec^{2}(x)(\tan(x)+3)dx
derivative sin(arcsin(x)+arccos(x))	derivative\:\sin(\arcsin(x)+\arccos(x))
(\partial)/(\partial x)(2(y-3)(x-2)^3)	\frac{\partial\:}{\partial\:x}(2(y-3)(x-2)^{3})
integral de (e^{8x}+e^{-9x})	\int\:(e^{8x}+e^{-9x})dx
derivative y=ln(3x^2+2x-1)	derivative\:y=\ln(3x^{2}+2x-1)
integral de (8e^{4sqrt(x)})/(sqrt(x))	\int\:\frac{8e^{4\sqrt{x}}}{\sqrt{x}}dx
derivative y= 2/(1-x^2)	derivative\:y=\frac{2}{1-x^{2}}
derivada de sin(2x+cos(2x))	\frac{d}{dx}(\sin(2x)+\cos(2x))
límite cuando x tiende a 3 de xsqrt(25-x^2)	\lim\:_{x\to\:3}(x\sqrt{25-x^{2}})
(\partial)/(\partial x)(e^y)	\frac{\partial\:}{\partial\:x}(e^{y})
integral de 2sin(4x)	\int\:2\sin(4x)dx
derivative f(x)=sqrt(x-4)	derivative\:f(x)=\sqrt{x-4}
(\partial)/(\partial x)(2/(2x+4y+1))	\frac{\partial\:}{\partial\:x}(\frac{2}{2x+4y+1})
derivada de 3sin(xcos^2(x)+sin^3(x))	\frac{d}{dx}(3\sin(x)\cos^{2}(x)+\sin^{3}(x))
(2xy^2+2y)dx+(2x^2y+2x)dy=0	(2xy^{2}+2y)dx+(2x^{2}y+2x)dy=0
(\partial)/(\partial x)(100e^{(-x-2y)})	\frac{\partial\:}{\partial\:x}(100e^{(-x-2y)})
límite cuando x tiende a 1 de g(x)(f(x))	\lim\:_{x\to\:1}(g(x)(f(x)))
límite cuando x tiende a 4 de ((3x^2-17x+20))/(4x^2-25x+36)	\lim\:_{x\to\:4}(\frac{(3x^{2}-17x+20)}{4x^{2}-25x+36})
integral de (ln(cos(x)))/(cos^2(x))	\int\:\frac{\ln(\cos(x))}{\cos^{2}(x)}dx
taylor 1/(sin(x))	taylor\:\frac{1}{\sin(x)}
taylor f(x)=e^{-2x}	taylor\:f(x)=e^{-2x}
derivative e^{x+9}	derivative\:e^{x+9}
1/(x^2)(dy)/(dx)=25+14y	\frac{1}{x^{2}}\frac{dy}{dx}=25+14y

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