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Problemas populares de Cálculo

implicit (dy)/(dx),x^2-xy+y^2=19	implicit\:\frac{dy}{dx},x^{2}-xy+y^{2}=19
(\partial)/(\partial x)((5s-3t)/(4s+5t))	\frac{\partial\:}{\partial\:x}(\frac{5s-3t}{4s+5t})
límite cuando x tiende a 0-de (7e^x)/(x^5)	\lim\:_{x\to\:0-}(\frac{7e^{x}}{x^{5}})
(dy)/(dx)=(xy+3x-y-3)/(xy-2x+4y-8)	\frac{dy}{dx}=\frac{xy+3x-y-3}{xy-2x+4y-8}
(3ln(x))^'	(3\ln(x))^{\prime\:}
derivada de sin(1/(x^2-5))	\frac{d}{dx}(\sin(\frac{1}{x^{2}-5}))
derivada de ln(1/(cos(x)))	\frac{d}{dx}(\ln(\frac{1}{\cos(x)}))
límite cuando x tiende a a de 0/0	\lim\:_{x\to\:a}(\frac{0}{0})
integral de (x^2)/(x^6-4)	\int\:\frac{x^{2}}{x^{6}-4}dx
(\partial)/(\partial x)(xe^{sqrt(6xy)})	\frac{\partial\:}{\partial\:x}(xe^{\sqrt{6xy}})
integral de 0 a infinity de 2/(x^2+4)	\int\:_{0}^{\infty\:}\frac{2}{x^{2}+4}dx
(1+x^2)(dy)/(dx)+3xy=5x	(1+x^{2})\frac{dy}{dx}+3xy=5x
y^2(dy)/(dx)=1	y^{2}\frac{dy}{dx}=1
integral de xarctan(20x)	\int\:x\arctan(20x)dx
derivative x/(x^2-2)	derivative\:\frac{x}{x^{2}-2}
integral de (3x^2+5)cos(7x)	\int\:(3x^{2}+5)\cos(7x)dx
derivative x^7*e^x	derivative\:x^{7}\cdot\:e^{x}
(\partial)/(\partial x)(x^6y^9-x^5y^8)	\frac{\partial\:}{\partial\:x}(x^{6}y^{9}-x^{5}y^{8})
(\partial)/(\partial x)(x-1/x e^{y/x})	\frac{\partial\:}{\partial\:x}(x-\frac{1}{x}e^{\frac{y}{x}})
d/(ds)(2/(s+sqrt(s^2+4)))	\frac{d}{ds}(\frac{2}{s+\sqrt{s^{2}+4}})
(\partial)/(\partial x)(6xy-12x)	\frac{\partial\:}{\partial\:x}(6xy-12x)
(2x+4)dx+(3y-1)dy=0	(2x+4)dx+(3y-1)dy=0
límite cuando x tiende a 0 de 1/(x+3)	\lim\:_{x\to\:0}(\frac{1}{x+3})
integral de cos^4(2x)sin(2x)	\int\:\cos^{4}(2x)\sin(2x)dx
derivada de (cos(x)/(x^2))	\frac{d}{dx}(\frac{\cos(x)}{x^{2}})
límite cuando x tiende a-6 de-12	\lim\:_{x\to\:-6}(-12)
d/(dθ)(1-cos(θ))	\frac{d}{dθ}(1-\cos(θ))
integral de 1/(x(x-3))	\int\:\frac{1}{x(x-3)}dx
derivative f(x)=10x^3	derivative\:f(x)=10x^{3}
integral de ((ln(x))^{34})/x	\int\:\frac{(\ln(x))^{34}}{x}dx
serie de n=1 a infinity de n/(n^2+5)	\sum\:_{n=1}^{\infty\:}\frac{n}{n^{2}+5}
(dy)/(dx)=(y+2)/(x-1)	\frac{dy}{dx}=\frac{y+2}{x-1}
derivada de e^{xln(a})	\frac{d}{dx}(e^{x\ln(a)})
derivative y=3x(6x-5x^2)	derivative\:y=3x(6x-5x^{2})
y^{''}-y^'-12y=0	y^{\prime\:\prime\:}-y^{\prime\:}-12y=0
integral de x/(x^2+x+1)	\int\:\frac{x}{x^{2}+x+1}dx
derivada de ((3x-1/(x^2+3))^2)	\frac{d}{dx}((\frac{3x-1}{x^{2}+3})^{2})
integral de 1 a 2 de 1/t	\int\:_{1}^{2}\frac{1}{t}dt
integral de (x^2-3x+3)	\int\:(x^{2}-3x+3)dx
integral de e^x+sin(y)	\int\:e^{x}+\sin(y)dx
límite cuando x tiende a 0 de (1+bx)^{1/x}	\lim\:_{x\to\:0}((1+bx)^{\frac{1}{x}})
integral de t^2+(2t-1)/(t^2-2t+1)	\int\:t^{2}+\frac{2t-1}{t^{2}-2t+1}dt
límite cuando x tiende a-1 de 1/(1+x^2)	\lim\:_{x\to\:-1}(\frac{1}{1+x^{2}})
derivative arcsin(9x+1)	derivative\:\arcsin(9x+1)
integral de 1/(x^{4/5)}	\int\:\frac{1}{x^{\frac{4}{5}}}dx
integral de 2 a infinity de 1/x	\int\:_{2}^{\infty\:}\frac{1}{x}dx
integral de-2.5-1/8 q	\int\:-2.5-\frac{1}{8}qdq
derivada de e^{sqrt(sec(x^2)})	\frac{d}{dx}(e^{\sqrt{\sec(x^{2})}})
límite cuando x tiende a 0+de (ln(x+1))/x	\lim\:_{x\to\:0+}(\frac{\ln(x+1)}{x})
derivative sin(3x)+cos(8x)	derivative\:\sin(3x)+\cos(8x)
(1+x^2)((dy)/(dx))-2xy=0	(1+x^{2})(\frac{dy}{dx})-2xy=0
integral de pi/2 a pi de x-sin(x)	\int\:_{\frac{π}{2}}^{π}x-\sin(x)dx
(dy)/(dx)=(3x)/(4y)	\frac{dy}{dx}=\frac{3x}{4y}
derivative sec(3sin(2x))	derivative\:\sec(3\sin(2x))
límite cuando x tiende a 0 de e^x-1	\lim\:_{x\to\:0}(e^{x}-1)
pendienteintercept (-3,-7),(2,3)	slopeintercept\:(-3,-7),(2,3)
integral de 1/(cos^2(s))	\int\:\frac{1}{\cos^{2}(s)}ds
derivada de (16x/((x^2+4)^2))	\frac{d}{dx}(\frac{16x}{(x^{2}+4)^{2}})
(\partial)/(\partial x)(3arctan(y/x))	\frac{\partial\:}{\partial\:x}(3\arctan(\frac{y}{x}))
integral de (sec(x)tan(x))/(sec(x)-5)	\int\:\frac{\sec(x)\tan(x)}{\sec(x)-5}dx
d/(dy)(x/y)	\frac{d}{dy}(\frac{x}{y})
área x^2-7x-24,-x^2+3x+4	area\:x^{2}-7x-24,-x^{2}+3x+4
(\partial)/(\partial y)(sqrt(x-y))	\frac{\partial\:}{\partial\:y}(\sqrt{x-y})
derivada de 6/(\sqrt[3]{x})	\frac{d}{dx}(\frac{6}{\sqrt[3]{x}})
derivative 3ln(5x)	derivative\:3\ln(5x)
x^2+2xy+x(dy)/(dx)=0	x^{2}+2xy+x\frac{dy}{dx}=0
derivative 3x^4-65x^3	derivative\:3x^{4}-65x^{3}
integral de 2sec^4(x)	\int\:2\sec^{4}(x)dx
integral de-(5000)/(x^2)	\int\:-\frac{5000}{x^{2}}dx
derivada de 2^x+3^x	\frac{d}{dx}(2^{x}+3^{x})
derivative-5t(3t^8-1)^7	derivative\:-5t(3t^{8}-1)^{7}
derivada de (3x^2+5x/(sqrt(x)))	\frac{d}{dx}(\frac{3x^{2}+5x}{\sqrt{x}})
(ds}{\frac{dt)/2}=sqrt(s)	\frac{ds}{\frac{dt}{2}}=\sqrt{s}
(d^{10})/(dx^{10)}(cos(2x))	\frac{d^{10}}{dx^{10}}(\cos(2x))
t^2*(dx)/(dt)= 1/x	t^{2}\cdot\:\frac{dx}{dt}=\frac{1}{x}
derivada de 8xe^{4x}	\frac{d}{dx}(8xe^{4x})
integral de (sin^2(x))/(x^2)	\int\:\frac{\sin^{2}(x)}{x^{2}}dx
derivative f(x)=(e^x)/(1-e^x)	derivative\:f(x)=\frac{e^{x}}{1-e^{x}}
15y^{''}-7y^'-4y=0	15y^{\prime\:\prime\:}-7y^{\prime\:}-4y=0
límite cuando t tiende a 0 de tan(4t)	\lim\:_{t\to\:0}(\tan(4t))
integral de 2t-3sin(t)	\int\:2t-3\sin(t)dt
derivada de 6x^2-7x	\frac{d}{dx}(6x^{2}-7x)
(dy}{dx}=\frac{3y)/x	\frac{dy}{dx}=\frac{3y}{x}
integral de x^{-4}(x+1)	\int\:x^{-4}(x+1)dx
derivada de (x^2-2^2)	\frac{d}{dx}((x^{2}-2)^{2})
integral de 1 a 3 de 6/x	\int\:_{1}^{3}\frac{6}{x}dx
derivative f(x)=4xsin(x)cos(x)	derivative\:f(x)=4x\sin(x)\cos(x)
pendiente (-3,-10),(4,5)	slope\:(-3,-10),(4,5)
derivative y=5x^4f(x)	derivative\:y=5x^{4}f(x)
20y^{''}-y^'+7y=0	20y^{\prime\:\prime\:}-y^{\prime\:}+7y=0
derivada de n/x	\frac{d}{dx}(\frac{n}{x})
derivada de ln((x+2^3))	\frac{d}{dx}(\ln((x+2)^{3}))
f^'(t)-f(t)=-8t	f^{\prime\:}(t)-f(t)=-8t
integral de e^{i6x}cos(4x)	\int\:e^{i6x}\cos(4x)dx
integral de sqrt(1+(-tan(x))^2)	\int\:\sqrt{1+(-\tan(x))^{2}}dx
(\partial)/(\partial v)(v/u)	\frac{\partial\:}{\partial\:v}(\frac{v}{u})
derivative sqrt(1/(x^{17))}	derivative\:\sqrt{\frac{1}{x^{17}}}
integral de-2 a 0 de (x^2)/(16/3)	\int\:_{-2}^{0}\frac{x^{2}}{\frac{16}{3}}dx
límite cuando x tiende a 1 de (x^2)/(1-x^2)	\lim\:_{x\to\:1}(\frac{x^{2}}{1-x^{2}})
d/(dt)(6t^3)	\frac{d}{dt}(6t^{3})

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