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Problemas populares de Cálculo

d/(dt)(e^{-at}cos(xt))	\frac{d}{dt}(e^{-at}\cos(xt))
y^'=(2x^5e^{y/x}+x^3y^2)/(x^4y)	y^{\prime\:}=\frac{2x^{5}e^{\frac{y}{x}}+x^{3}y^{2}}{x^{4}y}
tangent f(x)=-2x^2+4x-4,\at x=3	tangent\:f(x)=-2x^{2}+4x-4,\at\:x=3
(\partial)/(\partial x)(sqrt(x+3y))	\frac{\partial\:}{\partial\:x}(\sqrt{x+3y})
(log_{e}(x))^'	(\log_{e}(x))^{\prime\:}
pendiente (-3,5),(3,5)	slope\:(-3,5),(3,5)
y^'=2x+3	y^{\prime\:}=2x+3
64y^{''}-48y^'+34y=0	64y^{\prime\:\prime\:}-48y^{\prime\:}+34y=0
derivada de ln((x^2+1^{20}))	\frac{d}{dx}(\ln((x^{2}+1)^{20}))
integral de (x^2)/((x+1)(x-1)^2)	\int\:\frac{x^{2}}{(x+1)(x-1)^{2}}dx
integral de 1 a 2 de x^{-3}	\int\:_{1}^{2}x^{-3}dx
ty^'+(t+1)y=t	ty^{\prime\:}+(t+1)y=t
integral de 6x(3x^2-2)^4	\int\:6x(3x^{2}-2)^{4}dx
integral de 0 a 1/5 de 4arcsin(5y)	\int\:_{0}^{\frac{1}{5}}4\arcsin(5y)dy
tangent y=3x-4x^2,(-2,-22)	tangent\:y=3x-4x^{2},(-2,-22)
(\partial)/(\partial x)(e^{-xy}cos(y))	\frac{\partial\:}{\partial\:x}(e^{-xy}\cos(y))
inversalaplace 1/(s^2(s^2+3s+10))	inverselaplace\:\frac{1}{s^{2}(s^{2}+3s+10)}
derivada de (4e^{2x}-2e^x+1/(2e^{2x)})	\frac{d}{dx}(\frac{4e^{2x}-2e^{x}+1}{2e^{2x}})
integral de 3x^2e^x	\int\:3x^{2}e^{x}dx
(\partial)/(\partial x)(-2ycsc^3(x))	\frac{\partial\:}{\partial\:x}(-2y\csc^{3}(x))
derivada de 2cos^2(x^2+2)	\frac{d}{dx}(2\cos^{2}(x^{2}+2))
integral de 3/2 xe^{-6x}	\int\:\frac{3}{2}xe^{-6x}dx
derivative 6+1/5 sin(6pit)	derivative\:6+\frac{1}{5}\sin(6πt)
límite cuando x tiende a 0 de (1+3x)^{2/x}	\lim\:_{x\to\:0}((1+3x)^{\frac{2}{x}})
integral de (x^3)/(sqrt(x^2+144))	\int\:\frac{x^{3}}{\sqrt{x^{2}+144}}dx
(\partial)/(\partial x)(ln(2x^2))	\frac{\partial\:}{\partial\:x}(\ln(2x^{2}))
derivada de ((x^3)/3)	\frac{d}{dx}(\frac{(x^{3})}{3})
integral de v/(g-kv^2)	\int\:\frac{v}{g-kv^{2}}dv
integral de 4sin^3(x)cos^7(x)	\int\:4\sin^{3}(x)\cos^{7}(x)dx
integral de (x^2-y^2)	\int\:(x^{2}-y^{2})dx
límite cuando x tiende a 1 de ln(5x)+e^x	\lim\:_{x\to\:1}(\ln(5x)+e^{x})
integral de (1/(x^2-1))	\int\:(\frac{1}{x^{2}-1})dx
y^{''}-36y=0	y^{\prime\:\prime\:}-36y=0
d/(dt)((2t)/(1+t^2))	\frac{d}{dt}(\frac{2t}{1+t^{2}})
integral de-3 a 3 de 6/(x^2+9)	\int\:_{-3}^{3}\frac{6}{x^{2}+9}dx
integral de x^9*e^{x^{10}-9}	\int\:x^{9}\cdot\:e^{x^{10}-9}dx
normal y= x/(1+x^2),(2, 2/5)	normal\:y=\frac{x}{1+x^{2}},(2,\frac{2}{5})
serie de n=0 a infinity de e^{-(9n)/2}	\sum\:_{n=0}^{\infty\:}e^{-\frac{9n}{2}}
integral de u^{-3}	\int\:u^{-3}du
d/(dt)(t^{3/2})	\frac{d}{dt}(t^{\frac{3}{2}})
(dy)/(dx)=(x-3)e^{-2y}	\frac{dy}{dx}=(x-3)e^{-2y}
desarrollar (xsinh(x)+cos(x))^5	expand\:(x\sinh(x)+\cos(x))^{5}
integral de ln(t+1)	\int\:\ln(t+1)dt
integral de (-5)/(sqrt(4-2x-x^2))	\int\:\frac{-5}{\sqrt{4-2x-x^{2}}}dx
derivada de (sin(x)/(x^5))	\frac{d}{dx}(\frac{\sin(x)}{x^{5}})
derivada de x^4-2x^2+3	\frac{d}{dx}(x^{4}-2x^{2}+3)
tangent x^3-2x+1	tangent\:x^{3}-2x+1
tangent y=(x^3-9x)^{10},(3,0)	tangent\:y=(x^{3}-9x)^{10},(3,0)
tangent y=3x^3-3x,(-4,0)	tangent\:y=3x^{3}-3x,(-4,0)
integral de 0 a 3 de (5-5/3 x)^2	\int\:_{0}^{3}(5-\frac{5}{3}x)^{2}dx
pendiente (-10.6)(-5.8)	slope\:(-10.6)(-5.8)
derivada de sqrt(5x-x^2)	\frac{d}{dx}(\sqrt{5x-x^{2}})
límite cuando x tiende a 3 de 7	\lim\:_{x\to\:3}(7)
límite cuando x tiende a 1+de (x^2-1)/(x-1)	\lim\:_{x\to\:1+}(\frac{x^{2}-1}{x-1})
y^'=(2-e^x)/(3+2y)	y^{\prime\:}=\frac{2-e^{x}}{3+2y}
límite cuando x tiende a 7 de (x-7)/(sqrt(x-4)-\sqrt{3)}	\lim\:_{x\to\:7}(\frac{x-7}{\sqrt{x-4}-\sqrt{3}})
integral de e^{(-x)/(10)}	\int\:e^{\frac{-x}{10}}dx
tangent y=2x^3-x^2+6,(2,18)	tangent\:y=2x^{3}-x^{2}+6,(2,18)
y^'= y/x+tan(y/x)	y^{\prime\:}=\frac{y}{x}+\tan(\frac{y}{x})
4y^{''}+9y=0,y(0)=2,y^'(0)=3	4y^{\prime\:\prime\:}+9y=0,y(0)=2,y^{\prime\:}(0)=3
(\partial)/(\partial x)(xe^{-ax^2})	\frac{\partial\:}{\partial\:x}(xe^{-ax^{2}})
derivada de a(2e^{-3x}x-3e^{-3x}x^2)	\frac{d}{dx}(a(2e^{-3x}x-3e^{-3x}x^{2}))
(\partial)/(\partial x)(-sin(4x))	\frac{\partial\:}{\partial\:x}(-\sin(4x))
derivative f(x)=sqrt(x^2+2x+3)	derivative\:f(x)=\sqrt{x^{2}+2x+3}
integral de 4 x/((x+2)^{(1/4))}	\int\:4\frac{x}{(x+2)^{(\frac{1}{4})}}dx
límite cuando x tiende a 1-de 3^{1/x}	\lim\:_{x\to\:1-}(3^{\frac{1}{x}})
(\partial)/(\partial y)(e^x+cos(y+z))	\frac{\partial\:}{\partial\:y}(e^{x}+\cos(y+z))
(x^2+4)y^'+3xy=x	(x^{2}+4)y^{\prime\:}+3xy=x
serie de n=1 a infinity de 7/(4^n)	\sum\:_{n=1}^{\infty\:}\frac{7}{4^{n}}
límite cuando x tiende a 0 de (e^{ax}-1)/x	\lim\:_{x\to\:0}(\frac{e^{ax}-1}{x})
derivative x-asqrt(x)	derivative\:x-a\sqrt{x}
derivative sin^4(a)cos^9(a)	derivative\:\sin^{4}(a)\cos^{9}(a)
integral de 13e^{-13x}	\int\:13e^{-13x}dx
derivada de-1x	\frac{d}{dx}(-1x)
(\partial)/(\partial y)(xsec(y))	\frac{\partial\:}{\partial\:y}(x\sec(y))
límite cuando x tiende a 8-de 4x-2	\lim\:_{x\to\:8-}(4x-2)
integral de (7/(x^3))	\int\:(\frac{7}{x^{3}})dx
(\partial)/(\partial x)(x^3e^{sqrt(5xy)})	\frac{\partial\:}{\partial\:x}(x^{3}e^{\sqrt{5xy}})
(\partial)/(\partial x)(((7x+4))/(4y+1))	\frac{\partial\:}{\partial\:x}(\frac{(7x+4)}{4y+1})
derivative (e^{4x})^2	derivative\:(e^{4x})^{2}
y^'+2y=50e^{-10t}	y^{\prime\:}+2y=50e^{-10t}
derivada de (-x/(x^2+1))	\frac{d}{dx}(\frac{-x}{x^{2}+1})
inversalaplace 4/(s^2(s+1))	inverselaplace\:\frac{4}{s^{2}(s+1)}
y^{''}+7y^'+10y=13te^{5t}	y^{\prime\:\prime\:}+7y^{\prime\:}+10y=13te^{5t}
integral de x^3(1-x)	\int\:x^{3}(1-x)dx
integral de cos(x/4)	\int\:\cos(\frac{x}{4})dx
integral de-x^2-4	\int\:-x^{2}-4dx
(\partial)/(\partial x)(sin^3(x))	\frac{\partial\:}{\partial\:x}(\sin^{3}(x))
(x^7)^'	(x^{7})^{\prime\:}
integral de 1/(x*ln(2x))	\int\:\frac{1}{x\cdot\:\ln(2x)}dx
integral de xsqrt(3x+2)	\int\:x\sqrt{3x+2}dx
(dy)/(dx)=(2x+xy^2)/(4y+yx^2)	\frac{dy}{dx}=\frac{2x+xy^{2}}{4y+yx^{2}}
integral de 0 a 1/2 de 6arccos(x)	\int\:_{0}^{\frac{1}{2}}6\arccos(x)dx
límite cuando x tiende a infinity de 55^x	\lim\:_{x\to\:\infty\:}(55^{x})
integral de (2z+1)^3	\int\:(2z+1)^{3}dz
tangent y=(1+3x)^{10},(0,1)	tangent\:y=(1+3x)^{10},(0,1)
límite cuando x tiende a 0 de 2e^{5x}	\lim\:_{x\to\:0}(2e^{5x})
integral de 0 a 7 de-30x^2+340x	\int\:_{0}^{7}-30x^{2}+340xdx
límite cuando x tiende a+0 de 1/(sqrt(x-1))	\lim\:_{x\to\:+0}(\frac{1}{\sqrt{x-1}})
(x^2-y^2)dx+3xydy=0	(x^{2}-y^{2})dx+3xydy=0

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