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Problemas populares de Cálculo

y^'(t)=(y+1)*(y-3),y(0)=1	y^{\prime\:}(t)=(y+1)\cdot\:(y-3),y(0)=1
derivada de log_{10}(sin(x))	\frac{d}{dx}(\log_{10}(\sin(x)))
límite cuando x tiende a-4 de sqrt(5x+20)-8	\lim\:_{x\to\:-4}(\sqrt{5x+20}-8)
integral de 1/2 (x+1/2 sin(2x))	\int\:\frac{1}{2}(x+\frac{1}{2}\sin(2x))dx
límite cuando x tiende a 1 de x^2-2x	\lim\:_{x\to\:1}(x^{2}-2x)
(\partial)/(\partial y)(x^2-5xy+3y^2)	\frac{\partial\:}{\partial\:y}(x^{2}-5xy+3y^{2})
límite cuando x tiende a-2 de (2x-1)^2	\lim\:_{x\to\:-2}((2x-1)^{2})
integral de 4x^2-16x+16	\int\:4x^{2}-16x+16dx
límite cuando x tiende a 1 de (x^4-1)/(x-1)	\lim\:_{x\to\:1}(\frac{x^{4}-1}{x-1})
tangent f(-2)=2x^4	tangent\:f(-2)=2x^{4}
derivada de (4x+1^2)	\frac{d}{dx}((4x+1)^{2})
derivada de 1/((1-2x))	\frac{d}{dx}(\frac{1}{(1-2x)})
derivative e^{4t}	derivative\:e^{4t}
derivada de 2x^4+x^3+5x^2-3x+8	\frac{d}{dx}(2x^{4}+x^{3}+5x^{2}-3x+8)
derivada de x^2*e^{-3x}	\frac{d}{dx}(x^{2}\cdot\:e^{-3x})
(e^tx+1)dt+(e^t-1)dx=0,x(1)=1	(e^{t}x+1)dt+(e^{t}-1)dx=0,x(1)=1
límite cuando x tiende a 1 de log_{1/e}(x)	\lim\:_{x\to\:1}(\log_{\frac{1}{e}}(x))
laplacetransformación t*e^{5t}sin(3t)	laplacetransform\:t\cdot\:e^{5t}\sin(3t)
(\partial)/(\partial y)(1-xy)	\frac{\partial\:}{\partial\:y}(1-xy)
inversalaplace 1/(s(s^2+4))+1	inverselaplace\:\frac{1}{s(s^{2}+4)}+1
límite cuando x tiende a 0 de (4/(x-1)+4)/x	\lim\:_{x\to\:0}(\frac{\frac{4}{x-1}+4}{x})
derivada de sqrt(x/(x+2))	\frac{d}{dx}(\sqrt{\frac{x}{x+2}})
derivative e^{4xsin(2x)}	derivative\:e^{4x\sin(2x)}
derivative f(x)=x^3+5x	derivative\:f(x)=x^{3}+5x
(\partial)/(\partial x)(4e^{4xy})	\frac{\partial\:}{\partial\:x}(4e^{4xy})
laplacetransformación te^t	laplacetransform\:te^{t}
derivada de e^{x^4}+7x	\frac{d}{dx}(e^{x^{4}}+7x)
normal f(x)=sqrt(x^2+16),\at x=3	normal\:f(x)=\sqrt{x^{2}+16},\at\:x=3
integral de (e^{8x})/(e^{8x)+6}	\int\:\frac{e^{8x}}{e^{8x}+6}dx
límite cuando y tiende a 1 de (2sqrt(y^2+3))/(y-1)	\lim\:_{y\to\:1}(\frac{2\sqrt{y^{2}+3}}{y-1})
d/(dt)(2e^{-t}t-e^{-t}t^2)	\frac{d}{dt}(2e^{-t}t-e^{-t}t^{2})
derivative f(x)=ln(2x^5(5x-1)^3)	derivative\:f(x)=\ln(2x^{5}(5x-1)^{3})
derivative y=sqrt(3x+1)	derivative\:y=\sqrt{3x+1}
derivada de (9x^6+4x^3^4)	\frac{d}{dx}((9x^{6}+4x^{3})^{4})
límite cuando t tiende a pi de sin(3/4 t)	\lim\:_{t\to\:π}(\sin(\frac{3}{4}t))
derivative (ln(x))^{5cos(x)}	derivative\:(\ln(x))^{5\cos(x)}
pendiente (-4,7),(2,-8)	slope\:(-4,7),(2,-8)
límite cuando x tiende a 1+de (1-x)*tan((pix)/2)	\lim\:_{x\to\:1+}((1-x)\cdot\:\tan(\frac{πx}{2}))
integral de 1/(sqrt(5x^2-10x+10))	\int\:\frac{1}{\sqrt{5x^{2}-10x+10}}dx
(\partial)/(\partial y)((x^2y^2)/(x+y))	\frac{\partial\:}{\partial\:y}(\frac{x^{2}y^{2}}{x+y})
área y^2=x,x-y=2	area\:y^{2}=x,x-y=2
derivada de 2e^x+2/(\sqrt[3]{x})	\frac{d}{dx}(2e^{x}+\frac{2}{\sqrt[3]{x}})
integral de (4x)/((x^2+3)^2)	\int\:\frac{4x}{(x^{2}+3)^{2}}dx
tangent f(x)= 4/x ,\at x=2	tangent\:f(x)=\frac{4}{x},\at\:x=2
integral de 1/(x(ln(x^5)))	\int\:\frac{1}{x(\ln(x^{5}))}dx
(\partial)/(\partial y)(ln(x)+y^3x)	\frac{\partial\:}{\partial\:y}(\ln(x)+y^{3}x)
integral de (2-x)/(x^2+x)	\int\:\frac{2-x}{x^{2}+x}dx
integral de 4 a 16 de 1/(8-sqrt(x))	\int\:_{4}^{16}\frac{1}{8-\sqrt{x}}dx
límite cuando x tiende a 2+de 8/(x-2)	\lim\:_{x\to\:2+}(\frac{8}{x-2})
tangent f(x)=8x^2-x^3,(2,24)	tangent\:f(x)=8x^{2}-x^{3},(2,24)
pendiente (3,4),(5,8)	slope\:(3,4),(5,8)
y^'=(2y)/(3x)	y^{\prime\:}=\frac{2y}{3x}
integral de (x+6)/(x^2+11x+18)	\int\:\frac{x+6}{x^{2}+11x+18}dx
derivative 1/(2+x)	derivative\:\frac{1}{2+x}
límite cuando t tiende a 0 de (tan(5t))k	\lim\:_{t\to\:0}((\tan(5t))k)
taylor z/(z^{4+9)}	taylor\:\frac{z}{z^{4+9}}
integral de (5x^4)/4+(3x^2)/2+7x+C	\int\:\frac{5x^{4}}{4}+\frac{3x^{2}}{2}+7x+Cdx
inversalaplace (s+1)/((s+1)^2+1)	inverselaplace\:\frac{s+1}{(s+1)^{2}+1}
integral de (11x)^2	\int\:(11x)^{2}dx
integral de 1/((x+4)^{7/2)}	\int\:\frac{1}{(x+4)^{\frac{7}{2}}}dx
y^'+2xy=1	y^{\prime\:}+2xy=1
(-2)^'	(-2)^{\prime\:}
(\partial)/(\partial x)(e^t)	\frac{\partial\:}{\partial\:x}(e^{t})
límite cuando x tiende a 1 de x^3-2x+2	\lim\:_{x\to\:1}(x^{3}-2x+2)
integral de 2/(4x+7sqrt(x))	\int\:\frac{2}{4x+7\sqrt{x}}dx
(dy)/(dt)=y^2+k	\frac{dy}{dt}=y^{2}+k
integral de (e^x)/(sqrt(1-e^x))	\int\:\frac{e^{x}}{\sqrt{1-e^{x}}}dx
límite cuando x tiende a 1 de ln(x^2-1)	\lim\:_{x\to\:1}(\ln(x^{2}-1))
inversalaplace 1/(s^2+3s)	inverselaplace\:\frac{1}{s^{2}+3s}
límite cuando x tiende a pi-de (x+pi)csc(x)	\lim\:_{x\to\:π-}((x+π)\csc(x))
derivada de 2xe^x-e^{2x}	\frac{d}{dx}(2xe^{x}-e^{2x})
derivada de (2x^3+2(x^4-3x))	\frac{d}{dx}((2x^{3}+2)(x^{4}-3x))
tangent f(x)= x/(1+x^2),(3,0.3)	tangent\:f(x)=\frac{x}{1+x^{2}},(3,0.3)
inversalaplace ((1))/((s-3)(s+1))	inverselaplace\:\frac{(1)}{(s-3)(s+1)}
integral de (sqrt(25x^2-1))/x	\int\:\frac{\sqrt{25x^{2}-1}}{x}dx
integral de 2(x+20)e^{x/(20)}	\int\:2(x+20)e^{\frac{x}{20}}dx
derivada de xcos(4x)	\frac{d}{dx}(x\cos(4x))
integral de (t^4+1)/(t^5+4t^3)	\int\:\frac{t^{4}+1}{t^{5}+4t^{3}}dt
(x^2+1)y^'+9x(y-1)=0,y(0)=4	(x^{2}+1)y^{\prime\:}+9x(y-1)=0,y(0)=4
integral de u^2sqrt(u^3+2)	\int\:u^{2}\sqrt{u^{3}+2}du
taylor sin(x^7)	taylor\:\sin(x^{7})
y+2t^2+y^'tln(t)=0	y+2t^{2}+y^{\prime\:}t\ln(t)=0
integral de (x+8)/(x^2+16)	\int\:\frac{x+8}{x^{2}+16}dx
(\partial)/(\partial y)(3x^2-2xy+2)	\frac{\partial\:}{\partial\:y}(3x^{2}-2xy+2)
(\partial)/(\partial x)(ln((3xy)/(5z)))	\frac{\partial\:}{\partial\:x}(\ln(\frac{3xy}{5z}))
integral de (2x+1)sqrt(x-5)	\int\:(2x+1)\sqrt{x-5}dx
área \|4x-1\|,x^2-5	area\:\left\|4x-1\right\|,x^{2}-5
(dy)/(dx)=-((y^2)/(1+y^2)e^{(-x)})	\frac{dy}{dx}=-(\frac{y^{2}}{1+y^{2}}e^{(-x)})
límite cuando x tiende a 4 de 7	\lim\:_{x\to\:4}(7)
límite cuando x tiende a 0 de 1/8+x-(1/8)	\lim\:_{x\to\:0}(\frac{1}{8}+x-(\frac{1}{8}))
integral de (5x^2+3x-10)	\int\:(5x^{2}+3x-10)dx
integral de (18x^2)/(x^4-41x^2+400)	\int\:\frac{18x^{2}}{x^{4}-41x^{2}+400}dx
derivada de 4x-x^2-3	\frac{d}{dx}(4x-x^{2}-3)
límite cuando y tiende a 15 de sqrt(y+3)	\lim\:_{y\to\:15}(\sqrt{y+3})
integral de (sin(2e^{-4x}))/(e^{4x)}	\int\:\frac{\sin(2e^{-4x})}{e^{4x}}dx
área f(x)=x^3-3x^2+3x,g(x)=x	area\:f(x)=x^{3}-3x^{2}+3x,g(x)=x
derivative f(3)=2x^2+4x	derivative\:f(3)=2x^{2}+4x
integral de 1/(x^2sqrt(25x^2+64))	\int\:\frac{1}{x^{2}\sqrt{25x^{2}+64}}dx
(\partial)/(\partial y)(-3x^2y)	\frac{\partial\:}{\partial\:y}(-3x^{2}y)
área f(x)=x^2+4x,g(x)=x+10	area\:f(x)=x^{2}+4x,g(x)=x+10

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