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Problemas populares de Cálculo

(dy)/(dx)=(3x+xy^2)/(y+x^2y)	\frac{dy}{dx}=\frac{3x+xy^{2}}{y+x^{2}y}
integral de (e^{-x})/(1-e^{-2x)}	\int\:\frac{e^{-x}}{1-e^{-2x}}dx
(\partial)/(\partial x)(x^2-y^2+x+1)	\frac{\partial\:}{\partial\:x}(x^{2}-y^{2}+x+1)
derivative (2x^2+4x+6)/(sqrt(x))	derivative\:\frac{2x^{2}+4x+6}{\sqrt{x}}
derivada de x^2+2x-1	\frac{d}{dx}(x^{2}+2x-1)
-4(dy)/(dx)+12x^2=0	-4\frac{dy}{dx}+12x^{2}=0
derivative y=2x-3	derivative\:y=2x-3
área y=x+6,y=x^3,x=0	area\:y=x+6,y=x^{3},x=0
derivada de a^{-x}	\frac{d}{dx}(a^{-x})
d/(dt)(sqrt(3t+1))	\frac{d}{dt}(\sqrt{3t+1})
integral de-tln(t)	\int\:-t\ln(t)dt
tangent x^2,\at x=0	tangent\:x^{2},\at\:x=0
(\partial)/(\partial y)(x^3yz^2)	\frac{\partial\:}{\partial\:y}(x^{3}yz^{2})
integral de [ 4/(16x^2+1)]	\int\:[\frac{4}{16x^{2}+1}]dx
tangent f(x)=x^2-5x+5,(6,11)	tangent\:f(x)=x^{2}-5x+5,(6,11)
(\partial)/(\partial s)(s+t)	\frac{\partial\:}{\partial\:s}(s+t)
derivada de (x-3^{2/3})	\frac{d}{dx}((x-3)^{\frac{2}{3}})
integral de (2x)/(4-x^4)	\int\:\frac{2x}{4-x^{4}}dx
derivada de ln(sqrt(x^3))	\frac{d}{dx}(\ln(\sqrt{x^{3}}))
derivada de (1/2 x^5)	\frac{d}{dx}((\frac{1}{2}x)^{5})
límite cuando x tiende a infinity de (x)^{(ln(2))/(1+ln(x))}	\lim\:_{x\to\:\infty\:}((x)^{\frac{\ln(2)}{1+\ln(x)}})
derivative f(x)=(100)/((1+5x)^3)	derivative\:f(x)=\frac{100}{(1+5x)^{3}}
integral de x^3+sin(x)+cos(x)	\int\:x^{3}+\sin(x)+\cos(x)dx
integral de e^{8x}sin(9x)	\int\:e^{8x}\sin(9x)dx
derivative f(x)=tan^2(3e^x)	derivative\:f(x)=\tan^{2}(3e^{x})
derivative 7/((2x+1)^2)	derivative\:\frac{7}{(2x+1)^{2}}
x^{''}=-x+0.1x^'	x^{\prime\:\prime\:}=-x+0.1x^{\prime\:}
(y^{''}+10y^'+149)/(4y)=0	\frac{y^{\prime\:\prime\:}+10y^{\prime\:}+149}{4y}=0
límite cuando x tiende a 2 de+f(x)	\lim\:_{x\to\:2}(+f(x))
integral de (2x-3)/(x^2+10x+29)	\int\:\frac{2x-3}{x^{2}+10x+29}dx
derivada de x+cot(x/2)	\frac{d}{dx}(x+\cot(\frac{x}{2}))
(\partial)/(\partial y)(10xye^{-x^2-y^2})	\frac{\partial\:}{\partial\:y}(10xye^{-x^{2}-y^{2}})
derivada de-3cot(1-x^2)	\frac{d}{dx}(-3\cot(1-x^{2}))
límite cuando x tiende a 0 de 3-1/x	\lim\:_{x\to\:0}(3-\frac{1}{x})
f(x)=pi^x	f(x)=π^{x}
derivada de xsqrt(x^2-3x+2)	\frac{d}{dx}(x\sqrt{x^{2}-3x+2})
integral de sqrt(9x-5)	\int\:\sqrt{9x-5}dx
límite cuando x tiende a-1 de 6x+5	\lim\:_{x\to\:-1}(6x+5)
derivada de arccos(x/(sqrt(1-x^2)))	\frac{d}{dx}(\arccos(\frac{x}{\sqrt{1-x^{2}}}))
f(x)=cos^6(x)	f(x)=\cos^{6}(x)
límite cuando x tiende a 4 de x(x+5)(x+6)	\lim\:_{x\to\:4}(x(x+5)(x+6))
(d^4)/(dx^4)(3ln(x))	\frac{d^{4}}{dx^{4}}(3\ln(x))
(\partial)/(\partial x)((x^2+y^2)^6)	\frac{\partial\:}{\partial\:x}((x^{2}+y^{2})^{6})
límite cuando x tiende a 5 de 3	\lim\:_{x\to\:5}(3)
(xdy)/(dx)-y=3x^4	\frac{xdy}{dx}-y=3x^{4}
y^{''}-6y^'+25y=e^t	y^{\prime\:\prime\:}-6y^{\prime\:}+25y=e^{t}
integral de x^3arctan(x)	\int\:x^{3}\arctan(x)dx
d/(dθ)(θsin(θ))	\frac{d}{dθ}(θ\sin(θ))
tangent x^2+3x-2	tangent\:x^{2}+3x-2
(d^3)/(dx^3)(arctan(x))	\frac{d^{3}}{dx^{3}}(\arctan(x))
derivative-0.1x^2-x+40	derivative\:-0.1x^{2}-x+40
integral de 7xe^{(3x-1)}	\int\:7xe^{(3x-1)}dx
serie de n=1 a infinity de (n!)/(108^n)	\sum\:_{n=1}^{\infty\:}\frac{n!}{108^{n}}
y+xy^'=a(1+xy)	y+xy^{\prime\:}=a(1+xy)
derivada de (2x+5^7)	\frac{d}{dx}((2x+5)^{7})
y^'=(12(2y-1))/((3x-2)^2),y(2)=0	y^{\prime\:}=\frac{12(2y-1)}{(3x-2)^{2}},y(2)=0
integral de x^3cos(3x)	\int\:x^{3}\cos(3x)dx
límite cuando x tiende a+0 de sin(7x)	\lim\:_{x\to\:+0}(\sin(7x))
derivative (5x+6)(6x-7)	derivative\:(5x+6)(6x-7)
(dy)/(dx)-(1+x)(1+y^2)=0	\frac{dy}{dx}-(1+x)(1+y^{2})=0
integral de sqrt(12+4x-x^2)	\int\:\sqrt{12+4x-x^{2}}dx
área f(x)=2x^2+3,(-1,2)	area\:f(x)=2x^{2}+3,(-1,2)
límite cuando x tiende a 2 de 3x^2-1	\lim\:_{x\to\:2}(3x^{2}-1)
límite cuando x tiende a 5+de (x+1)/(x-5)	\lim\:_{x\to\:5+}(\frac{x+1}{x-5})
tangent f(x)=8e^x+x,\at x=8	tangent\:f(x)=8e^{x}+x,\at\:x=8
límite cuando x tiende a infinity de-1+e^{(x+1)}	\lim\:_{x\to\:\infty\:}(-1+e^{(x+1)})
límite cuando x tiende a infinity de (6)^x	\lim\:_{x\to\:\infty\:}((6)^{x})
integral de (x^4e^x-4x^3)/(x^4)	\int\:\frac{x^{4}e^{x}-4x^{3}}{x^{4}}dx
y^'=9.8-0.2y,y(0)=100	y^{\prime\:}=9.8-0.2y,y(0)=100
serie de n=-4 a infinity de (-4/9)^n	\sum\:_{n=-4}^{\infty\:}(-\frac{4}{9})^{n}
límite cuando x tiende a 5+de (x-5)/(\|x-5\|)	\lim\:_{x\to\:5+}(\frac{x-5}{\left\|x-5\right\|})
y^'=-y/(2000)4	y^{\prime\:}=-\frac{y}{2000}4
área y=\sqrt[3]{x},y= 1/x ,x=8,(1,1)	area\:y=\sqrt[3]{x},y=\frac{1}{x},x=8,(1,1)
pendiente (-4,0),(0,-1)	slope\:(-4,0),(0,-1)
integral de 3(t+1)^{1/2}	\int\:3(t+1)^{\frac{1}{2}}dt
límite cuando x tiende a 0.5 de 3x^2+2x-3	\lim\:_{x\to\:0.5}(3x^{2}+2x-3)
(\partial)/(\partial x)(x^{1/3}y^{2/3})	\frac{\partial\:}{\partial\:x}(x^{\frac{1}{3}}y^{\frac{2}{3}})
área x^2,-x^2+4x	area\:x^{2},-x^{2}+4x
integral de 1/(2-5x)	\int\:\frac{1}{2-5x}dx
límite cuando x tiende a 0 de x(x-1)	\lim\:_{x\to\:0}(x(x-1))
derivative f(x)=arctan(x)+arctan(1/x)	derivative\:f(x)=\arctan(x)+\arctan(\frac{1}{x})
f(x)=ln(sin(x))	f(x)=\ln(\sin(x))
derivative (12)/(sqrt(t))	derivative\:\frac{12}{\sqrt{t}}
límite cuando x tiende a 0+de (tan(9x))^x	\lim\:_{x\to\:0+}((\tan(9x))^{x})
integral de 1/(x^3-4x)	\int\:\frac{1}{x^{3}-4x}dx
integral de (3x^2+1)/((x^2-1)^3)	\int\:\frac{3x^{2}+1}{(x^{2}-1)^{3}}dx
derivative 8sin(8x-1)	derivative\:8\sin(8x-1)
derivada de e^x(2x+3^3)	\frac{d}{dx}(e^{x}(2x+3)^{3})
(d^2)/(dx^2)(e^{3/x})	\frac{d^{2}}{dx^{2}}(e^{\frac{3}{x}})
integral de (9x)/(x^2+1)	\int\:\frac{9x}{x^{2}+1}dx
tangent f(x)=6sqrt(x),\at x=1	tangent\:f(x)=6\sqrt{x},\at\:x=1
(16y^2-xy)dx+x^2dy=0	(16y^{2}-xy)dx+x^{2}dy=0
derivada de \sqrt[9]{x}-3/x	\frac{d}{dx}(\sqrt[9]{x}-\frac{3}{x})
derivada de 2^xtan(3x)	\frac{d}{dx}(2^{x}\tan(3x))
(\partial)/(\partial z)(xy+2z)	\frac{\partial\:}{\partial\:z}(xy+2z)
(\partial)/(\partial x)(5xy-18x)	\frac{\partial\:}{\partial\:x}(5xy-18x)
derivada de (7x+8(8x-9))	\frac{d}{dx}((7x+8)(8x-9))
integral de (sqrt(x^2-225))/x	\int\:\frac{\sqrt{x^{2}-225}}{x}dx
y^'=2xsqrt(1-y^2)	y^{\prime\:}=2x\sqrt{1-y^{2}}
derivada de (Ax+Be^x)	\frac{d}{dx}((Ax+B)e^{x})

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