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Problemas populares de Cálculo

y^'=(ty^2-1)y	y^{\prime\:}=(ty^{2}-1)y
tangent-2x^2,\at 1	tangent\:-2x^{2},\at\:1
derivada de e^{x^3+5x}	\frac{d}{dx}(e^{x^{3}+5x})
integral de ((sin^2(x)))/(cos(x))	\int\:\frac{(\sin^{2}(x))}{\cos(x)}dx
integral de csc(x)cot^2(x)	\int\:\csc(x)\cot^{2}(x)dx
derivada de 6^{2x}	\frac{d}{dx}(6^{2x})
(e^{8x})^'	(e^{8x})^{\prime\:}
derivada de x^2-8,x	\frac{d}{dx}(x^{2}-8,x)
límite cuando x tiende a 0+de ln(x)+1/x	\lim\:_{x\to\:0+}(\ln(x)+\frac{1}{x})
(\partial)/(\partial x)(x/(x+3y))	\frac{\partial\:}{\partial\:x}(\frac{x}{x+3y})
derivada de 43^{sqrt(x)}	\frac{d}{dx}(43^{\sqrt{x}})
serie de n=1 a infinity}(2^{-n de)/n	\sum\:_{n=1}^{\infty\:}\frac{2^{-n}}{n}
derivada de ax+e^{ax}	\frac{d}{dx}(ax+e^{ax})
integral de 28x^3-18x^2+8x	\int\:28x^{3}-18x^{2}+8xdx
integral de 5e^{8x}	\int\:5e^{8x}dx
(cos(sqrt(x)))^'	(\cos(\sqrt{x}))^{\prime\:}
integral de (e^x-e^{-x})/(e^{2x)}	\int\:\frac{e^{x}-e^{-x}}{e^{2x}}dx
límite cuando x tiende a 3 de [3(8)(-10)]	\lim\:_{x\to\:3}([3(8)(-10)])
integral de 8/(t+1)+t	\int\:\frac{8}{t+1}+tdt
derivada de e^{xy}= derivada de 2y	\frac{d}{dx}(e^{xy})=\frac{d}{dx}(2y)
(\partial)/(\partial x)(-e^{-x}y-e^{-x})	\frac{\partial\:}{\partial\:x}(-e^{-x}y-e^{-x})
derivative f(x)=((480t)/((t^2+5)^3))	derivative\:f(x)=(\frac{480t}{(t^{2}+5)^{3}})
integral de (x(y^2-5y+6))/(x^2+1)	\int\:\frac{x(y^{2}-5y+6)}{x^{2}+1}dx
límite cuando x tiende a 5 de in(x^2-25)	\lim\:_{x\to\:5}(in(x^{2}-25))
integral de 1/(sqrt(x+1)-\sqrt{x)}	\int\:\frac{1}{\sqrt{x+1}-\sqrt{x}}dx
límite cuando x tiende a 1 de ((x))/(x-1)	\lim\:_{x\to\:1}(\frac{(x)}{x-1})
integral de (x+1)/((x^2+2x)^2)	\int\:\frac{x+1}{(x^{2}+2x)^{2}}dx
derivada de arccsc(-5x^2)	\frac{d}{dx}(\arccsc(-5x^{2}))
límite cuando x tiende a-infinity de (12)/x	\lim\:_{x\to\:-\infty\:}(\frac{12}{x})
integral de (3x-5)/(x^2-4x+3)	\int\:\frac{3x-5}{x^{2}-4x+3}dx
(dy)/(dx)+y/x =y^2	\frac{dy}{dx}+\frac{y}{x}=y^{2}
integral de x^3+2x^2-x+k	\int\:x^{3}+2x^{2}-x+kdx
(\partial)/(\partial y)(y^2+2e^{x^2}xy)	\frac{\partial\:}{\partial\:y}(y^{2}+2e^{x^{2}}xy)
integral de (sqrt(1+x))/(sqrt(1-x))	\int\:\frac{\sqrt{1+x}}{\sqrt{1-x}}dx
(\partial)/(\partial y)(ln(2x+y+1))	\frac{\partial\:}{\partial\:y}(\ln(2x+y+1))
integral de-4e^{-x/4}	\int\:-4e^{-\frac{x}{4}}dx
límite cuando (x,y) tiende a (2,1) de (x-2y)/(x^3-8y^3)	\lim\:_{(x,y)\to\:(2,1)}(\frac{x-2y}{x^{3}-8y^{3}})
(\partial)/(\partial y)(y^4sin(6x))	\frac{\partial\:}{\partial\:y}(y^{4}\sin(6x))
integral de 1/(u(u+2))	\int\:\frac{1}{u(u+2)}du
tangent 2x^2+x-1	tangent\:2x^{2}+x-1
y^{''}+4y=4cos(2t)	y^{\prime\:\prime\:}+4y=4\cos(2t)
integral de 9/((7x+4)^5)	\int\:\frac{9}{(7x+4)^{5}}dx
integral de 2x^2cos(5x)	\int\:2x^{2}\cos(5x)dx
y^'+7y=5cos(2t)	y^{\prime\:}+7y=5\cos(2t)
y^{''}-2y^'+2y=2x-2	y^{\prime\:\prime\:}-2y^{\prime\:}+2y=2x-2
límite cuando x tiende a 0+de 2^{-1/x}	\lim\:_{x\to\:0+}(2^{-\frac{1}{x}})
integral de 1/((x^2+y^2+z^2)^{3/2)}	\int\:\frac{1}{(x^{2}+y^{2}+z^{2})^{\frac{3}{2}}}dx
integral de (4x^2+x+27)/(x^3+9x)	\int\:\frac{4x^{2}+x+27}{x^{3}+9x}dx
(\partial)/(\partial x)(2x^2-7y^9-4)	\frac{\partial\:}{\partial\:x}(2x^{2}-7y^{9}-4)
derivative e^xsin(x)+e^xcos(x)	derivative\:e^{x}\sin(x)+e^{x}\cos(x)
integral de ysqrt(y^2+1)	\int\:y\sqrt{y^{2}+1}dy
límite cuando x tiende a 3 de 2x+4	\lim\:_{x\to\:3}(2x+4)
integral de (e^x)/(\sqrt[3]{e^x+2)}	\int\:\frac{e^{x}}{\sqrt[3]{e^{x}+2}}dx
derivada de (x^2+3(x^2-4x))	\frac{d}{dx}((x^{2}+3)(x^{2}-4x))
serie de n=0 a infinity de 2*0.3^n	\sum\:_{n=0}^{\infty\:}2\cdot\:0.3^{n}
(dy)/(dx)+x(y^2+y)=0	\frac{dy}{dx}+x(y^{2}+y)=0
integral de (2tan(x))/(1-tan^2(x))	\int\:\frac{2\tan(x)}{1-\tan^{2}(x)}dx
derivada de tan(2x+1)	\frac{d}{dx}(\tan(2x+1))
tangent y=x^3+6x	tangent\:y=x^{3}+6x
inversalaplace 4+x^6	inverselaplace\:4+x^{6}
f(x)=2xsqrt(4-x^2)	f(x)=2x\sqrt{4-x^{2}}
límite cuando x tiende a 2 de-x^2+6x-4	\lim\:_{x\to\:2}(-x^{2}+6x-4)
área y=sqrt(6x-2),(1,3)	area\:y=\sqrt{6x-2},(1,3)
f(x)=sqrt((2x)/(x+1))	f(x)=\sqrt{\frac{2x}{x+1}}
derivada de (x+2/(x^2-4))	\frac{d}{dx}(\frac{x+2}{x^{2}-4})
derivada de (6x^2+2x+8/(sqrt(x)))	\frac{d}{dx}(\frac{6x^{2}+2x+8}{\sqrt{x}})
tangent y=3x^3-x^2+8,(2,28)	tangent\:y=3x^{3}-x^{2}+8,(2,28)
derivada de (ln(x)/2)	\frac{d}{dx}(\frac{\ln(x)}{2})
integral de asin(θ)(1+sin(θ))	\int\:a\sin(θ)(1+\sin(θ))dθ
área 3/x ,12x, x/3	area\:\frac{3}{x},12x,\frac{x}{3}
integral de (t^2-2cos(t))	\int\:(t^{2}-2\cos(t))dt
derivative f(x)=2x^2-3x+1	derivative\:f(x)=2x^{2}-3x+1
límite cuando x tiende a 0 de (100)/(x^2)	\lim\:_{x\to\:0}(\frac{100}{x^{2}})
d/(dt)(e^{2t})	\frac{d}{dt}(e^{2t})
integral de (x-6)sin(pix)	\int\:(x-6)\sin(πx)dx
derivative cos^3(t)	derivative\:\cos^{3}(t)
derivada de (-3/(x^4))	\frac{d}{dx}(\frac{-3}{x^{4}})
integral de 0 a pi de 4cos^4(x)sin(x)	\int\:_{0}^{π}4\cos^{4}(x)\sin(x)dx
tangent 18e^x+15x	tangent\:18e^{x}+15x
derivada de sqrt(3e^{x+1)}	\frac{d}{dx}(\sqrt{3e^{x+1}})
(ln(x^2))^'	(\ln(x^{2}))^{\prime\:}
derivada de ((2)/((6-12x)))	\frac{d}{dx}(\frac{(2)}{(6-12x)})
área 5cos(pix),12x^2-3,-0.5,0.5	area\:5\cos(πx),12x^{2}-3,-0.5,0.5
derivada de 2yx	\frac{d}{dx}(2yx)
(\partial)/(\partial x)(4x^2y^3+2)	\frac{\partial\:}{\partial\:x}(4x^{2}y^{3}+2)
inversalaplace 1/(s(s^2+7s+12))	inverselaplace\:\frac{1}{s(s^{2}+7s+12)}
integral de sin^2(x)*cos^3(x)	\int\:\sin^{2}(x)\cdot\:\cos^{3}(x)dx
fouriertransformación x^2	fouriertransform\:x^{2}
derivada de (5x-1/((6x^2-2)^2))	\frac{d}{dx}(\frac{5x-1}{(6x^{2}-2)^{2}})
derivada de ln(x/4*(x-4))	\frac{d}{dx}(\ln(\frac{x}{4})\cdot\:(x-4))
derivada de 1/2 (1-cos(2x))	\frac{d}{dx}(\frac{1}{2}(1-\cos(2x)))
integral de (16)/(x^2-4)	\int\:\frac{16}{x^{2}-4}dx
área-10x+11,x^2-5x-13	area\:-10x+11,x^{2}-5x-13
tangent y=(5x)/((x+1)^2),(0,0)	tangent\:y=\frac{5x}{(x+1)^{2}},(0,0)
xy^'+y^2=0	xy^{\prime\:}+y^{2}=0
integral de sqrt(-x)	\int\:\sqrt{-x}dx
(\partial)/(\partial x)(y*arctan(x/z))	\frac{\partial\:}{\partial\:x}(y\cdot\:\arctan(\frac{x}{z}))
integral de ((x^3-1)/(x-1))	\int\:(\frac{x^{3}-1}{x-1})dx
derivada de sec(pi/6)	\frac{d}{dx}(\sec(\frac{π}{6}))
integral de x^2(x^3+8)^3	\int\:x^{2}(x^{3}+8)^{3}dx

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