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Problemas populares de Cálculo

implicit (dy)/(dx),e^{(x/y)}=6x-y	implicit\:\frac{dy}{dx},e^{(\frac{x}{y})}=6x-y
tangent (x-2)(x^2-10x+25)	tangent\:(x-2)(x^{2}-10x+25)
(dx)/(dy)=4(x^21),x(pi/4)=1	\frac{dx}{dy}=4(x^{2}1),x(\frac{π}{4})=1
(3x^2+y-4)-(2y-x)*(dy)/(dx)=0	(3x^{2}+y-4)-(2y-x)\cdot\:\frac{dy}{dx}=0
simplificar (x+1)^2(x^2+1)^{-3}	simplify\:(x+1)^{2}(x^{2}+1)^{-3}
(dy)/(dx)-y/x =-5/2 x^2y^3	\frac{dy}{dx}-\frac{y}{x}=-\frac{5}{2}x^{2}y^{3}
laplacetransformación 4(t-2)e^{4t}	laplacetransform\:4(t-2)e^{4t}
y^'+y/x = 1/x	y^{\prime\:}+\frac{y}{x}=\frac{1}{x}
(\partial)/(\partial x)(ln(2+sin(xy)))	\frac{\partial\:}{\partial\:x}(\ln(2+\sin(xy)))
(\partial)/(\partial z)(zx^2)	\frac{\partial\:}{\partial\:z}(zx^{2})
(dy)/(dx)=sin(x)(cos(2y)-cos^2(y))	\frac{dy}{dx}=\sin(x)(\cos(2y)-\cos^{2}(y))
serie de n=1 a infinity de (n-1)/(n!)	\sum\:_{n=1}^{\infty\:}\frac{n-1}{n!}
límite cuando x tiende a infinity de (e^{5x}+x^2)/(e^{5x)-x}	\lim\:_{x\to\:\infty\:}(\frac{e^{5x}+x^{2}}{e^{5x}-x})
d/(dt)(2sin^3(t))	\frac{d}{dt}(2\sin^{3}(t))
área y=(x+1)^2,(-1,0)	area\:y=(x+1)^{2},(-1,0)
integral de ke^{-2x}	\int\:ke^{-2x}dx
derivative y=(x-1)/(x+1)	derivative\:y=\frac{x-1}{x+1}
límite cuando x tiende a 0-de arccos(e^{-x^2})	\lim\:_{x\to\:0-}(\arccos(e^{-x^{2}}))
tangent (x+2)^2+(y-3)^2=37,(-3,-3)	tangent\:(x+2)^{2}+(y-3)^{2}=37,(-3,-3)
integral de 0 a pi/4 de 3cos^5(2x)	\int\:_{0}^{\frac{π}{4}}3\cos^{5}(2x)dx
integral de-2tcos(t)	\int\:-2t\cos(t)dt
integral de 48t^7e^{-t^8}	\int\:48t^{7}e^{-t^{8}}dt
integral de x(3x+10)^{49}	\int\:x(3x+10)^{49}dx
derivada de sqrt((x+39^2+(43+x)^2))	\frac{d}{dx}(\sqrt{(x+39)^{2}+(43+x)^{2}})
derivative ((x-3)(x^2+3x+9))/(x^3)	derivative\:\frac{(x-3)(x^{2}+3x+9)}{x^{3}}
x^2y(dy)/(dx)-9=0	x^{2}y\frac{dy}{dx}-9=0
integral de-13cos(x)	\int\:-13\cos(x)dx
d/(d{r)}(4/3 pi{r}^3)	\frac{d}{d{r}}(\frac{4}{3}π{r}^{3})
y^'-2y=e^{2t},y(0)=2	y^{\prime\:}-2y=e^{2t},y(0)=2
y^'+y=0	y^{\prime\:}+y=0
(ln(y))^'	(\ln(y))^{\prime\:}
(3x^2+y^2)/(y^2)dx-(2x^3+5y)/(y^3)dy=0	\frac{3x^{2}+y^{2}}{y^{2}}dx-\frac{2x^{3}+5y}{y^{3}}dy=0
derivada de 1/(sin(1/x))	\frac{d}{dx}(\frac{1}{\sin(\frac{1}{x})})
derivada de (4x/(5-cot(x)))	\frac{d}{dx}(\frac{4x}{5-\cot(x)})
integral de (e^t+2e^{2t})/(e^{3t)}	\int\:\frac{e^{t}+2e^{2t}}{e^{3t}}dt
(\partial)/(\partial x)(xe^{5y})	\frac{\partial\:}{\partial\:x}(xe^{5y})
derivada de 3x^2-4x	\frac{d}{dx}(3x^{2}-4x)
(\partial)/(\partial y)(2x^2y)	\frac{\partial\:}{\partial\:y}(2x^{2}y)
integral de 1 a 2 de xsin(pix)	\int\:_{1}^{2}x\sin(πx)dx
(dy)/(dt)+2y=e^{-t}cos(3t),y(0)=0	\frac{dy}{dt}+2y=e^{-t}\cos(3t),y(0)=0
integral de (16)/((64x^2+1)^2)	\int\:\frac{16}{(64x^{2}+1)^{2}}dx
área f(x)=(x+3)^3,[-1,6]	area\:f(x)=(x+3)^{3},[-1,6]
integral de 0 a 3 de x(3-x)	\int\:_{0}^{3}x(3-x)dx
integral de 2x^3(t^4-3)^5	\int\:2x^{3}(t^{4}-3)^{5}dx
inversalaplace 3/((s+1)(s+2))	inverselaplace\:\frac{3}{(s+1)(s+2)}
integral de (14x-11)/((2x-3)(x+1))	\int\:\frac{14x-11}{(2x-3)(x+1)}dx
integral de ln(y+1)	\int\:\ln(y+1)dy
derivative (s+3)/(4s^2+5)	derivative\:\frac{s+3}{4s^{2}+5}
límite cuando x tiende a 0+de 1/(x^{13)}	\lim\:_{x\to\:0+}(\frac{1}{x^{13}})
(\partial)/(\partial y)(x-1/y)	\frac{\partial\:}{\partial\:y}(x-\frac{1}{y})
pendiente (-1.2)(4.3)	slope\:(-1.2)(4.3)
y^'=-2ty^2	y^{\prime\:}=-2ty^{2}
integral de 0 a infinity de 1/(3+x)	\int\:_{0}^{\infty\:}\frac{1}{3+x}dx
serie de n=1 a infinity de 9/((-2)^n)	\sum\:_{n=1}^{\infty\:}\frac{9}{(-2)^{n}}
límite cuando x tiende a 1-de e^{1/(x-1)}	\lim\:_{x\to\:1-}(e^{\frac{1}{x-1}})
(\partial)/(\partial x)(8xy)	\frac{\partial\:}{\partial\:x}(8xy)
derivative y=e^{3tsin(2t)}	derivative\:y=e^{3t\sin(2t)}
integral de 1/((4x+5))	\int\:\frac{1}{(4x+5)}dx
integral de sin(2x)cos^2(2x)	\int\:\sin(2x)\cos^{2}(2x)dx
derivative G(r)=sqrt(r)+\sqrt[6]{r}	derivative\:G(r)=\sqrt{r}+\sqrt[6]{r}
x(dy)/(dx)=y-sqrt(x^2+y^2)	x\frac{dy}{dx}=y-\sqrt{x^{2}+y^{2}}
derivada de (10/(2x))	\frac{d}{dx}(\frac{10}{2x})
derivada de x/2 ln((1+x/(1-x))-1)	\frac{d}{dx}(\frac{x}{2}\ln(\frac{1+x}{1-x})-1)
derivative 8sin(2x)	derivative\:8\sin(2x)
derivada de (1+sqrt(x)/(x^4))	\frac{d}{dx}(\frac{1+\sqrt{x}}{x^{4}})
(\partial)/(\partial x)(5y^4cos(3x))	\frac{\partial\:}{\partial\:x}(5y^{4}\cos(3x))
derivada de (4x^3+6/x)	\frac{d}{dx}(\frac{4x^{3}+6}{x})
integral de 25 a 50 de 15	\int\:_{25}^{50}15dx
derivada de 3e^x+ln(x+tan(x))	\frac{d}{dx}(3e^{x}+\ln(x)+\tan(x))
límite cuando t tiende a 0 de 7/t-7/(t^2+t)	\lim\:_{t\to\:0}(\frac{7}{t}-\frac{7}{t^{2}+t})
límite cuando x tiende a 2 de (x^2)/(x-2)	\lim\:_{x\to\:2}(\frac{x^{2}}{x-2})
límite cuando x tiende a infinity de \sqrt[7]{x}	\lim\:_{x\to\:\infty\:}(\sqrt[7]{x})
integral de (\sqrt[3]{1+ln(x)})/x	\int\:\frac{\sqrt[3]{1+\ln(x)}}{x}dx
extreme f(x)=sqrt(r^2-11x^2)	extreme\:f(x)=\sqrt{r^{2}-11x^{2}}
(\partial)/(\partial u)(sqrt(u*v))	\frac{\partial\:}{\partial\:u}(\sqrt{u\cdot\:v})
derivative-1/4 cos^4(x)	derivative\:-\frac{1}{4}\cos^{4}(x)
integral de (x^4-3x^2)/(x^5-5x^3-24)	\int\:\frac{x^{4}-3x^{2}}{x^{5}-5x^{3}-24}dx
simplificar x/y	simplify\:\frac{x}{y}
integral de e^{-4x}sin(3x)	\int\:e^{-4x}\sin(3x)dx
integral de (x^3)/(3sqrt(1-x^2))	\int\:\frac{x^{3}}{3\sqrt{1-x^{2}}}dx
tangent f(x)=x+sqrt(x),\at x=36	tangent\:f(x)=x+\sqrt{x},\at\:x=36
integral de ((ln(x))^{10})/x	\int\:\frac{(\ln(x))^{10}}{x}dx
integral de (sin(x))/(sqrt(1))	\int\:\frac{\sin(x)}{\sqrt{1}}dx
derivada de 9^{sin(pix})	\frac{d}{dx}(9^{\sin(πx)})
derivada de-sin(x+cos(x)+x-1/(x^2))	\frac{d}{dx}(-\sin(x)+\cos(x)+x-\frac{1}{x^{2}})
tangent f(x)=sqrt(x+7),\at x=9	tangent\:f(x)=\sqrt{x+7},\at\:x=9
integral de tan(θ)4sin(2θ)	\int\:\tan(θ)4\sin(2θ)dθ
integral de 7/((z-10)^7)	\int\:\frac{7}{(z-10)^{7}}dz
integral de-1 a 1 de 3^x	\int\:_{-1}^{1}3^{x}dx
tangent f(x)=18sqrt(x),(9,54)	tangent\:f(x)=18\sqrt{x},(9,54)
derivada de (2x+5^3)	\frac{d}{dx}((2x+5)^{3})
y^'=xe^{x+y}	y^{\prime\:}=xe^{x+y}
derivada de x^3-3x^2-9x+4	\frac{d}{dx}(x^{3}-3x^{2}-9x+4)
inversalaplace s^{-3/2}	inverselaplace\:s^{-\frac{3}{2}}
integral de x^2-1	\int\:x^{2}-1dx
pendiente (-2.5)(-1.2)	slope\:(-2.5)(-1.2)
derivative y=ln(xsqrt(x^2-4))	derivative\:y=\ln(x\sqrt{x^{2}-4})
tangent f(x)=sqrt(x)+1/(sqrt(x^3))	tangent\:f(x)=\sqrt{x}+\frac{1}{\sqrt{x^{3}}}
integral de 3/(50+2t)	\int\:\frac{3}{50+2t}dt
derivada de-2cos(x+3x^3)	\frac{d}{dx}(-2\cos(x)+3x^{3})

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