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Problemas populares de Cálculo

y^'=((6t^2))/y	y^{\prime\:}=\frac{(6t^{2})}{y}
límite cuando x tiende a a de-6	\lim\:_{x\to\:a}(-6)
derivative-0.5cos(8t)	derivative\:-0.5\cos(8t)
(d^2y)/(dx^2)+2(dy)/(dx)+y=(e^x)/(x^2+1)	\frac{d^{2}y}{dx^{2}}+2\frac{dy}{dx}+y=\frac{e^{x}}{x^{2}+1}
derivada de (x^{3/2})	\frac{d}{dx}((x)^{\frac{3}{2}})
y^{''}-7y^'+6y=-4e^{-5t}	y^{\prime\:\prime\:}-7y^{\prime\:}+6y=-4e^{-5t}
derivative (\|x\|)/(sqrt(2-x^2))	derivative\:\frac{\left\|x\right\|}{\sqrt{2-x^{2}}}
(dy)/(dx)=((y^2))/(2x+3)	\frac{dy}{dx}=\frac{(y^{2})}{2x+3}
integral de ((x+2)/(sqrt(x)))	\int\:(\frac{x+2}{\sqrt{x}})dx
tangent f(x)=sqrt(3x+4),\at x=7	tangent\:f(x)=\sqrt{3x+4},\at\:x=7
integral de 3 a 4 de 1/((x-3)^3)	\int\:_{3}^{4}\frac{1}{(x-3)^{3}}dx
tangent f(x)=3x^{-2},\at x=4	tangent\:f(x)=3x^{-2},\at\:x=4
límite cuando x tiende a+0 de 1+sinh(2x)	\lim\:_{x\to\:+0}(1+\sinh(2x))
(dy)/(dx)=(6x)/(5y)	\frac{dy}{dx}=\frac{6x}{5y}
integral de 0 a pi^2 de sin(sqrt(x))	\int\:_{0}^{π^{2}}\sin(\sqrt{x})dx
límite cuando x tiende a infinity de 3x+1	\lim\:_{x\to\:\infty\:}(3x+1)
integral de x/(sqrt(x)+1)	\int\:\frac{x}{\sqrt{x}+1}dx
inversalaplace 4/S+6/(S^5)-1/(S+8)	inverselaplace\:\frac{4}{S}+\frac{6}{S^{5}}-\frac{1}{S+8}
derivada de-2/5 x^{5/2}+32x^{1/2}	\frac{d}{dx}(-\frac{2}{5}x^{\frac{5}{2}}+32x^{\frac{1}{2}})
derivada de xsqrt(x+8)	\frac{d}{dx}(x\sqrt{x+8})
integral de x^3-8x^2+16x+1	\int\:x^{3}-8x^{2}+16x+1dx
derivative 3x^{1/3}-5x^{4/3}	derivative\:3x^{\frac{1}{3}}-5x^{\frac{4}{3}}
integral de e^{7x+1}	\int\:e^{7x+1}dx
(\partial)/(\partial x)(sqrt((x+3)/(y+3)))	\frac{\partial\:}{\partial\:x}(\sqrt{\frac{x+3}{y+3}})
inversalaplace s/(s+a)	inverselaplace\:\frac{s}{s+a}
integral de 1/(x^2-2x+122)	\int\:\frac{1}{x^{2}-2x+122}dx
integral de (sin^7(5x))/(cos^4(5x))	\int\:\frac{\sin^{7}(5x)}{\cos^{4}(5x)}dx
d/(dt)(e^tcos(t))	\frac{d}{dt}(e^{t}\cos(t))
integral de tarcsec(t)	\int\:t\arcsec(t)dt
integral de (1+tan^2(x))	\int\:(1+\tan^{2}(x))dx
d/(dy)((y^2)/(y^2+1))	\frac{d}{dy}(\frac{y^{2}}{y^{2}+1})
pendiente (3,-3),(1,-1)	slope\:(3,-3),(1,-1)
(\partial)/(\partial x)(xe^{yz})	\frac{\partial\:}{\partial\:x}(xe^{yz})
integral de x/((x+1)^2(x^2+1))	\int\:\frac{x}{(x+1)^{2}(x^{2}+1)}dx
integral de 0 a 0.5 de 400x	\int\:_{0}^{0.5}400xdx
tangent f(x)=(1+2x)^{11},(0,1)	tangent\:f(x)=(1+2x)^{11},(0,1)
x^2y=(x^3+y^3)y^'	x^{2}y=(x^{3}+y^{3})y^{\prime\:}
(\partial)/(\partial x)((xz)/(sqrt(y^2-z)))	\frac{\partial\:}{\partial\:x}(\frac{xz}{\sqrt{y^{2}-z}})
taylor sec(x)	taylor\:\sec(x)
integral de x/(x^3+1)	\int\:\frac{x}{x^{3}+1}dx
integral de sin(x)+sin(x)cos(x)	\int\:\sin(x)+\sin(x)\cos(x)dx
integral de (4sqrt(x))/(x^3+1)	\int\:\frac{4\sqrt{x}}{x^{3}+1}dx
integral de (4x^2+1)^3*8x	\int\:(4x^{2}+1)^{3}\cdot\:8xdx
derivative sqrt(x)(1-x^2)	derivative\:\sqrt{x}(1-x^{2})
límite cuando x tiende a 2 de xsqrt(x^2-4)	\lim\:_{x\to\:2}(x\sqrt{x^{2}-4})
y^{''}+5y^'+y=0	y^{\prime\:\prime\:}+5y^{\prime\:}+y=0
integral de ((6x^2+4))/((3y^2-4))	\int\:\frac{(6x^{2}+4)}{(3y^{2}-4)}
(\partial)/(\partial x)(4x^8y^6+5x^7y^5)	\frac{\partial\:}{\partial\:x}(4x^{8}y^{6}+5x^{7}y^{5})
integral de-infinity a 8 de e^{0.04x}	\int\:_{-\infty\:}^{8}e^{0.04x}dx
derivative (t+e^t)(3-sqrt(t))	derivative\:(t+e^{t})(3-\sqrt{t})
límite cuando x tiende a 0 de x/(cos(x)-1)	\lim\:_{x\to\:0}(\frac{x}{\cos(x)-1})
límite cuando x tiende a 5 de 3x-3	\lim\:_{x\to\:5}(3x-3)
yln(x)(dy}{dx}=(\frac{y+1)/x)^2	y\ln(x)\frac{dy}{dx}=(\frac{y+1}{x})^{2}
derivada de (2x^2-5x/(3x+5))	\frac{d}{dx}(\frac{2x^{2}-5x}{3x+5})
límite cuando x tiende a 0+de 2^{1/x}	\lim\:_{x\to\:0+}(2^{\frac{1}{x}})
inversalaplace 2/(s(1+3s))	inverselaplace\:\frac{2}{s(1+3s)}
área x=-2,x=1,y=6x,y=x^2-7	area\:x=-2,x=1,y=6x,y=x^{2}-7
serie de n=1 a infinity de n^5(1+n^6)^2	\sum\:_{n=1}^{\infty\:}n^{5}(1+n^{6})^{2}
integral de e^{-x^2-2x+7}(x+1)	\int\:e^{-x^{2}-2x+7}(x+1)dx
y^{''}+16y=3sin(4t),y(0)=0,y^'(0)=0	y^{\prime\:\prime\:}+16y=3\sin(4t),y(0)=0,y^{\prime\:}(0)=0
tangent y=x^3-9x,(-3,0)	tangent\:y=x^{3}-9x,(-3,0)
integral de 0 a 1 de 7e^{x^2}	\int\:_{0}^{1}7e^{x^{2}}dx
derivada de (2x^2-1/(xsqrt(1+x^2)))	\frac{d}{dx}(\frac{2x^{2}-1}{x\sqrt{1+x^{2}}})
integral de (x^2)/(x-4)	\int\:\frac{x^{2}}{x-4}dx
derivative 5	derivative\:5
(dy)/(dx)+6(tan(6x))y=2*cos(6x)	\frac{dy}{dx}+6\cdot\:(\tan(6x))\cdot\:y=2\cdot\:\cos(6x)
integral de (33x^2)/(sqrt(x^2-4))	\int\:\frac{33x^{2}}{\sqrt{x^{2}-4}}dx
derivative (10-3x)/2	derivative\:\frac{10-3x}{2}
(\partial)/(\partial x)(2e^{xy+6})	\frac{\partial\:}{\partial\:x}(2e^{xy+6})
integral de 0 a pi de xcos^2(x)	\int\:_{0}^{π}x\cos^{2}(x)dx
límite cuando x tiende a 0 de (1-7x)^{1/x}	\lim\:_{x\to\:0}((1-7x)^{\frac{1}{x}})
integral de ((x^3-4x))/((x^2+1)^2)	\int\:\frac{(x^{3}-4x)}{(x^{2}+1)^{2}}dx
integral de 7x^4-5x^3+4x^2+C	\int\:7x^{4}-5x^{3}+4x^{2}+Cdx
(x+2)y^'-y= 3/(x+2)	(x+2)y^{\prime\:}-y=\frac{3}{x+2}
límite cuando x tiende a infinity+de 1/x	\lim\:_{x\to\:\infty\:+}(\frac{1}{x})
(t/y)dy+(1+ln(y))dt=0	(\frac{t}{y})dy+(1+\ln(y))dt=0
integral de 1/6 sec(x)tan(x)	\int\:\frac{1}{6}\sec(x)\tan(x)dx
integral de 5tan(3x)ln(sec(3x))	\int\:5\tan(3x)\ln(\sec(3x))dx
derivada de (a-b/x ^2)	\frac{d}{dx}((a-\frac{b}{x})^{2})
integral de 6xsqrt(3x^2-1)	\int\:6x\sqrt{3x^{2}-1}dx
serie de n=1 a infinity de 2/(n*(n+1))	\sum\:_{n=1}^{\infty\:}\frac{2}{n\cdot\:(n+1)}
integral de w^2	\int\:w^{2}dw
derivative g(x)=(4x^3+6x^2)^5	derivative\:g(x)=(4x^{3}+6x^{2})^{5}
d/(dθ)(2sin^2(θ))	\frac{d}{dθ}(2\sin^{2}(θ))
derivada de (ax-b(cx^2))	\frac{d}{dx}((ax-b)(cx^{2}))
límite cuando x tiende a-infinity de ((x^{-1}+x^{-4}))/(x^{-2)-x^{-3}}	\lim\:_{x\to\:-\infty\:}(\frac{(x^{-1}+x^{-4})}{x^{-2}-x^{-3}})
integral de sin(ln(9x))	\int\:\sin(\ln(9x))dx
(dy)/(dx)+2y=5	\frac{dy}{dx}+2y=5
tangent ln(2-x^2+2x^4)	tangent\:\ln(2-x^{2}+2x^{4})
y^'=2cos(t)+y/2	y^{\prime\:}=2\cos(t)+\frac{y}{2}
taylor xe^{2x}	taylor\:xe^{2x}
d/(dt)(cos(6t))	\frac{d}{dt}(\cos(6t))
límite cuando x tiende a 0 de x(cot(x))	\lim\:_{x\to\:0}(x(\cot(x)))
derivada de 11x^4cot(x)	\frac{d}{dx}(11x^{4}\cot(x))
área x^3+1,0,-2,1	area\:x^{3}+1,0,-2,1
integral de-3x*sin(x)	\int\:-3x\cdot\:\sin(x)dx
límite cuando x tiende a 3 de 2x-4	\lim\:_{x\to\:3}(2x-4)
integral de 0 a 4 de 3sqrt(x)-(3x)/2	\int\:_{0}^{4}3\sqrt{x}-\frac{3x}{2}dx
integral de xsec(x^2)	\int\:x\sec(x^{2})dx
tangent y=16sqrt(x),(4,32)	tangent\:y=16\sqrt{x},(4,32)

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