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Problemas populares de Cálculo

derivada de (e^{2x+1}/(2x+5))	\frac{d}{dx}(\frac{e^{2x+1}}{2x+5})
serie de n=1 a infinity de (ln(n))/(2n)	\sum\:_{n=1}^{\infty\:}\frac{\ln(n)}{2n}
área y= 3/x ,y=12x	area\:y=\frac{3}{x},y=12x
(\partial)/(\partial x)(y^{z/x})	\frac{\partial\:}{\partial\:x}(y^{\frac{z}{x}})
integral de ((8x-3))/((4x^2+(-3)x))	\int\:\frac{(8x-3)}{(4x^{2}+(-3)x)}dx
integral de x/((2+x^2))	\int\:\frac{x}{(2+x^{2})}dx
límite cuando x tiende a 1 de (1+8/(-1))^{-x}	\lim\:_{x\to\:1}((1+\frac{8}{-1})^{-x})
dx=xsqrt(x^2-16dy)	dx=x\sqrt{x^{2}-16dy}
derivative 6/(5x+2)	derivative\:\frac{6}{5x+2}
integral de \sqrt[3]{y}	\int\:\sqrt[3]{y}dy
(\partial)/(\partial y)(9-x^2-y^2)	\frac{\partial\:}{\partial\:y}(9-x^{2}-y^{2})
límite cuando x tiende a infinity de (10+9e^{(2x)})/(11-8e^{(3x))}	\lim\:_{x\to\:\infty\:}(\frac{10+9e^{(2x)}}{11-8e^{(3x)}})
integral de 0 a 5 de x	\int\:_{0}^{5}xdx
derivative ln(9sin^2(x))	derivative\:\ln(9\sin^{2}(x))
d/(du)((5u)/(4u^2+1))	\frac{d}{du}(\frac{5u}{4u^{2}+1})
tangent y= 1/x ,\at x=2	tangent\:y=\frac{1}{x},\at\:x=2
(\partial)/(\partial x)(x/(x^2+8y^2))	\frac{\partial\:}{\partial\:x}(\frac{x}{x^{2}+8y^{2}})
integral de 1/(ln(x+1))	\int\:\frac{1}{\ln(x+1)}dx
integral de 1/(x^2sqrt(10x+1))	\int\:\frac{1}{x^{2}\sqrt{10x+1}}dx
integral de e^θsin(θ)	\int\:e^{θ}\sin(θ)dθ
límite cuando x tiende a-2 de (-x-2)/(x+2)	\lim\:_{x\to\:-2}(\frac{-x-2}{x+2})
serie de n=1 a infinity}(((-3)^{n-1 de))/(5^n)	\sum\:_{n=1}^{\infty\:}\frac{((-3)^{n-1})}{5^{n}}
derivative f(x)=4(x-4)^2(x-1)	derivative\:f(x)=4(x-4)^{2}(x-1)
(\partial)/(\partial y)(xye^{xz})	\frac{\partial\:}{\partial\:y}(xye^{xz})
integral de 2sin^3(x)	\int\:2\sin^{3}(x)dx
límite cuando x tiende a infinity de xa	\lim\:_{x\to\:\infty\:}(xa)
integral de x/((x+2)(x+3))	\int\:\frac{x}{(x+2)(x+3)}dx
inversalaplace 1/(s^2)-(48)/(s^5)	inverselaplace\:\frac{1}{s^{2}}-\frac{48}{s^{5}}
derivada de (x^3-6/(x^2))	\frac{d}{dx}(\frac{x^{3}-6}{x^{2}})
área x=((y-2)^2)/3 ,y=8-x	area\:x=\frac{(y-2)^{2}}{3},y=8-x
integral de 1/(x^{1/2)+x^{1/3}}	\int\:\frac{1}{x^{\frac{1}{2}}+x^{\frac{1}{3}}}dx
integral de 4x^2-x+1	\int\:4x^{2}-x+1dx
derivada de arctan(sin(ln(x^3)))	\frac{d}{dx}(\arctan(\sin(\ln(x^{3}))))
(dy}{dx}=\frac{x^6-6y)/x	\frac{dy}{dx}=\frac{x^{6}-6y}{x}
integral de ((2x^2-x+3))/(sqrt(x))	\int\:\frac{(2x^{2}-x+3)}{\sqrt{x}}dx
integral de 0 a 1 de x(x^2+1)^5	\int\:_{0}^{1}x(x^{2}+1)^{5}dx
derivada de ((x^2+2/3)^2)	\frac{d}{dx}((\frac{x^{2}+2}{3})^{2})
pendiente y=2x^3-x^2+3	slope\:y=2x^{3}-x^{2}+3
(d^2)/(dx^2)(sqrt(x^2+4))	\frac{d^{2}}{dx^{2}}(\sqrt{x^{2}+4})
(dy)/(dx)=4xy	\frac{dy}{dx}=4xy
derivada de (sqrt(x)/(5+x))	\frac{d}{dx}(\frac{\sqrt{x}}{5+x})
integral de 0 a 3 de 1/(3x+1)	\int\:_{0}^{3}\frac{1}{3x+1}dx
integral de 1/(1+5x^2)	\int\:\frac{1}{1+5x^{2}}dx
derivative sqrt(3-5x)	derivative\:\sqrt{3-5x}
derivative x^2+5x+1	derivative\:x^{2}+5x+1
integral de cot(11t)sqrt(1-sin^2(11t))	\int\:\cot(11t)\sqrt{1-\sin^{2}(11t)}dt
derivative f(x)=ax^2+bx	derivative\:f(x)=ax^{2}+bx
integral de 2/(x^{0.85)}	\int\:\frac{2}{x^{0.85}}dx
(\partial)/(\partial x)(2xy+x{f}(x,y)(y/x))	\frac{\partial\:}{\partial\:x}(2xy+x{f}(x,y)(\frac{y}{x}))
(\partial)/(\partial y)(3+2xy)	\frac{\partial\:}{\partial\:y}(3+2xy)
área 5x,3x^2	area\:5x,3x^{2}
(\partial)/(\partial x)(2cos(x^2+y^2))	\frac{\partial\:}{\partial\:x}(2\cos(x^{2}+y^{2}))
(\partial)/(\partial u)(tan(u/v))	\frac{\partial\:}{\partial\:u}(\tan(\frac{u}{v}))
integral de (5x-2)/(x^2-x)	\int\:\frac{5x-2}{x^{2}-x}dx
área y=x^2,y=12-x	area\:y=x^{2},y=12-x
derivada de sqrt(x+13)	\frac{d}{dx}(\sqrt{x+13})
límite cuando x tiende a infinity de ln\|x\|	\lim\:_{x\to\:\infty\:}(\ln\left\|x\right\|)
y^{''}+81y=0,y(0)=4,y^'(0)=7	y^{\prime\:\prime\:}+81y=0,y(0)=4,y^{\prime\:}(0)=7
tangent y=(e^{2x}-2)^2,(0,1)	tangent\:y=(e^{2x}-2)^{2},(0,1)
implicit (dy)/(dx), y/x =0	implicit\:\frac{dy}{dx},\frac{y}{x}=0
(\partial)/(\partial x)(sin(h)(x^2+y))	\frac{\partial\:}{\partial\:x}(\sin(h)(x^{2}+y))
derivada de sqrt(-ln(x^2+y))	\frac{d}{dx}(\sqrt{-\ln(x^{2}+y)})
límite cuando x tiende a 7 de x	\lim\:_{x\to\:7}(x)
inversalaplace 1/(s^2+s+1)	inverselaplace\:\frac{1}{s^{2}+s+1}
integral de cos(x)(sec(x)tan(x))	\int\:\cos(x)(\sec(x)\tan(x))dx
límite cuando x tiende a-2 de (x+2)/(\|x+2\|)	\lim\:_{x\to\:-2}(\frac{x+2}{\left\|x+2\right\|})
límite cuando x tiende a 0 de ln(x)sin(x)	\lim\:_{x\to\:0}(\ln(x)\sin(x))
derivada de ln(sqrt(x-1))	\frac{d}{dx}(\ln(\sqrt{x-1}))
integral de-2 a 7 de ()((t-7)(1-t))	\int\:_{-2}^{7}\frac{d}{dt}((t-7)(1-t))dt
integral de 0 a 0.6 de 500x	\int\:_{0}^{0.6}500xdx
derivative (8x^3-5x+2)^pi	derivative\:(8x^{3}-5x+2)^{π}
(dx)/(dt)+x= 1/(t+1)	\frac{dx}{dt}+x=\frac{1}{t+1}
(\partial)/(\partial x)(cos(2x+5y+9z))	\frac{\partial\:}{\partial\:x}(\cos(2x+5y+9z))
tangent f(x)=-sin(x),\at x=0	tangent\:f(x)=-\sin(x),\at\:x=0
e^{x+y}y^'=x	e^{x+y}y^{\prime\:}=x
límite cuando x tiende a 5+de ln(sin(x))	\lim\:_{x\to\:5+}(\ln(\sin(x)))
y^'=((xy+2y))/(x+3)	y^{\prime\:}=\frac{(xy+2y)}{x+3}
desarrollar (2x+x^2)/((1+x)^2)	expand\:\frac{2x+x^{2}}{(1+x)^{2}}
(\partial)/(\partial x)(ln(1+3x^2y^3))	\frac{\partial\:}{\partial\:x}(\ln(1+3x^{2}y^{3}))
límite cuando x tiende a 3 de (x^2-9)/(x+3)	\lim\:_{x\to\:3}(\frac{x^{2}-9}{x+3})
integral de 8xcos^2(x)	\int\:8x\cos^{2}(x)dx
y^'+sin(t)y=-sin(t)	y^{\prime\:}+\sin(t)y=-\sin(t)
(\partial)/(\partial x)(arcsin(10xyz))	\frac{\partial\:}{\partial\:x}(\arcsin(10xyz))
tangent y=(1+x)/(1+e^x),(0, 1/2)	tangent\:y=\frac{1+x}{1+e^{x}},(0,\frac{1}{2})
límite cuando x tiende a 0+de 3xln(x)	\lim\:_{x\to\:0+}(3x\ln(x))
derivative sqrt(3x)ln(15x)	derivative\:\sqrt{3x}\ln(15x)
1=-sin(x-y) derivada de x-y	1=-\sin(x-y)\frac{d}{dx}(x-y)
límite cuando x tiende a 6 de (2x+7)/(x+3)	\lim\:_{x\to\:6}(\frac{2x+7}{x+3})
área x^2+2x+1,2x+5,[-2,2]	area\:x^{2}+2x+1,2x+5,[-2,2]
integral de 0 a pi de sin(3x)	\int\:_{0}^{π}\sin(3x)dx
(dy)/(dx)=y^2sin(x^2),y(-5)= 1/7	\frac{dy}{dx}=y^{2}\sin(x^{2}),y(-5)=\frac{1}{7}
derivada de (x-pisin(y)+sin(x)cos(y))	\frac{d}{dx}((x-π)\sin(y)+\sin(x)\cos(y))
derivative f(x)=2log_{5}(x)	derivative\:f(x)=2\log_{5}(x)
integral de 8/(2+8x)	\int\:\frac{8}{2+8x}dx
y^{''}-y=-sin(x)	y^{\prime\:\prime\:}-y=-\sin(x)
derivative 10sqrt(6x^9+9x^6)	derivative\:10\sqrt{6x^{9}+9x^{6}}
límite cuando x tiende a 2-de (x^2)/(x^2-4)	\lim\:_{x\to\:2-}(\frac{x^{2}}{x^{2}-4})
(\partial)/(\partial y)(xe^y-ye^x)	\frac{\partial\:}{\partial\:y}(xe^{y}-ye^{x})
(\partial)/(\partial x)(e^x-x^2arctan(x))	\frac{\partial\:}{\partial\:x}(e^{x}-x^{2}\arctan(x))
(6(t+1)dy)/(dt)-5y=5t,y(0)=4	\frac{6(t+1)dy}{dt}-5y=5t,y(0)=4

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