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Problemas populares de Cálculo

derivative sqrt(9+2x)	derivative\:\sqrt{9+2x}
integral de x^2y^3	\int\:x^{2}y^{3}dx
serie de n=1 a infinity de nx^{n-1}	\sum\:_{n=1}^{\infty\:}nx^{n-1}
integral de 3x^2e^{5x^3}	\int\:3x^{2}e^{5x^{3}}dx
serie de n=1 a infinity de (ln(9n))/n	\sum\:_{n=1}^{\infty\:}\frac{\ln(9n)}{n}
derivada de ln(1+9x)	\frac{d}{dx}(\ln(1+9x))
e^{-x}y(dy)/(dx)=e^{-y}+e^{-2x-y}	e^{-x}y\frac{dy}{dx}=e^{-y}+e^{-2x-y}
integral de 1/(sqrt(x^2-9))	\int\:\frac{1}{\sqrt{x^{2}-9}}dx
integral de (4e^{3x})/(1+e^{3x)}	\int\:\frac{4e^{3x}}{1+e^{3x}}dx
límite cuando x tiende a 0 de 1+3^x	\lim\:_{x\to\:0}(1+3^{x})
integral de x^2sqrt(x^3+7)	\int\:x^{2}\sqrt{x^{3}+7}dx
implicit (dy)/(dx),2x^2+2x+xy=1	implicit\:\frac{dy}{dx},2x^{2}+2x+xy=1
f(x)=e^x-x^e	f(x)=e^{x}-x^{e}
(\partial)/(\partial x)(A^2x^2+B^2y^2)	\frac{\partial\:}{\partial\:x}(A^{2}x^{2}+B^{2}y^{2})
derivada de (log_{10}(x)/x)	\frac{d}{dx}(\frac{\log_{10}(x)}{x})
integral de 1/(x(\sqrt[9]{x))}	\int\:\frac{1}{x(\sqrt[9]{x})}dx
serie de n=0 a infinity de 1/(0.5^n)	\sum\:_{n=0}^{\infty\:}\frac{1}{0.5^{n}}
(12-6y+e^{-3x})dx-2dy=0	(12-6y+e^{-3x})dx-2dy=0
integral de (x^3)/(x^4+10)	\int\:\frac{x^{3}}{x^{4}+10}dx
(sin^3(t))^'	(\sin^{3}(t))^{\prime\:}
y^{''}=-4y+e^x	y^{\prime\:\prime\:}=-4y+e^{x}
integral de (x^2-3x-8)/(x^2-2x+1)	\int\:\frac{x^{2}-3x-8}{x^{2}-2x+1}dx
pendiente xy-6y^2=4,(14,2)	slope\:xy-6y^{2}=4,(14,2)
integral de x^{n-1}sqrt(a+bx^n)	\int\:x^{n-1}\sqrt{a+bx^{n}}dx
derivada de x(x+4^2)	\frac{d}{dx}(x(x+4)^{2})
(\partial)/(\partial x)(10x^2y+5xy^3)	\frac{\partial\:}{\partial\:x}(10x^{2}y+5xy^{3})
derivada de (ln(x)^8)	\frac{d}{dx}((\ln(x))^{8})
y^{''}+4y^'+4y=((e^{2x}))/((x))	y^{\prime\:\prime\:}+4y^{\prime\:}+4y=\frac{(e^{2x})}{(x)}
derivative A/(y^8)+Be^y	derivative\:\frac{A}{y^{8}}+Be^{y}
integral de (x-5)/x	\int\:\frac{x-5}{x}dx
integral de 1 a 3 de 2x+1	\int\:_{1}^{3}2x+1dx
laplacetransformación 10sin(80pit)	laplacetransform\:10\sin(80πt)
(\partial)/(\partial x)(4/3 piy^2x)	\frac{\partial\:}{\partial\:x}(\frac{4}{3}πy^{2}x)
límite cuando x tiende a 2 de sqrt(x-1)	\lim\:_{x\to\:2}(\sqrt{x-1})
(\partial)/(\partial x)(4x^3-4x)	\frac{\partial\:}{\partial\:x}(4x^{3}-4x)
derivative pix	derivative\:πx
integral de 1/(sin(ax+b))	\int\:\frac{1}{\sin(ax+b)}dx
(dy)/(dx)=sqrt(6x+y)-6	\frac{dy}{dx}=\sqrt{6x+y}-6
integral de (7x^2+4x+7)/(x^3-1)	\int\:\frac{7x^{2}+4x+7}{x^{3}-1}dx
integral de-3 a 3 de ((18)/(9+x^2)-1)	\int\:_{-3}^{3}(\frac{18}{9+x^{2}}-1)dx
límite cuando x tiende a-infinity de \|x\|	\lim\:_{x\to\:-\infty\:}(\left\|x\right\|)
2(dy)/(dx)+4y=-8y^3	2\frac{dy}{dx}+4y=-8y^{3}
(\partial)/(\partial x)(3(y+4)(x-5)^3)	\frac{\partial\:}{\partial\:x}(3(y+4)(x-5)^{3})
derivada de x^2sqrt(2x-5)	\frac{d}{dx}(x^{2}\sqrt{2x-5})
integral de 1/(sqrt(2pi))e^{(-x^2)/2}	\int\:\frac{1}{\sqrt{2π}}e^{\frac{-x^{2}}{2}}dx
límite cuando x tiende a 0 de e^{x^3}	\lim\:_{x\to\:0}(e^{x^{3}})
integral de sin(4)(x)	\int\:\sin(4)(x)dx
taylor e^{1-x}	taylor\:e^{1-x}
integral de (1+t+t^2)/(sqrt(t))	\int\:\frac{1+t+t^{2}}{\sqrt{t}}dt
límite cuando h tiende a 0 de h/h	\lim\:_{h\to\:0}(\frac{h}{h})
derivative (x^4)/6-10x	derivative\:\frac{x^{4}}{6}-10x
derivada de (c^2-x^2/(c^2+x^2))	\frac{d}{dx}(\frac{c^{2}-x^{2}}{c^{2}+x^{2}})
derivative y=xsin(5/x)	derivative\:y=x\sin(\frac{5}{x})
f(x)=(cos(x))/(2+sin(x))	f(x)=\frac{\cos(x)}{2+\sin(x)}
integral de cos^3(8-x)sin(8-x)	\int\:\cos^{3}(8-x)\sin(8-x)dx
implicit (dy)/(dx),xy=5	implicit\:\frac{dy}{dx},xy=5
serie de n=0 a infinity de (5/6)^n	\sum\:_{n=0}^{\infty\:}(\frac{5}{6})^{n}
derivada de x^3+3x^2+1	\frac{d}{dx}(x^{3}+3x^{2}+1)
límite cuando x tiende a 0 de (x-4)/(x+2)	\lim\:_{x\to\:0}(\frac{x-4}{x+2})
límite cuando x tiende a 1 de ((x+2))/(x-1)	\lim\:_{x\to\:1}(\frac{(x+2)}{x-1})
tangent f(x)=2x^2+x+1,\at x=2	tangent\:f(x)=2x^{2}+x+1,\at\:x=2
(\partial)/(\partial x)(2arctan(y/x))	\frac{\partial\:}{\partial\:x}(2\arctan(\frac{y}{x}))
tangent y=7sec(x),\at x= pi/3	tangent\:y=7\sec(x),\at\:x=\frac{π}{3}
d/(dt)(arctan(t/2))	\frac{d}{dt}(\arctan(\frac{t}{2}))
derivative sqrt(x^2+5)	derivative\:\sqrt{x^{2}+5}
derivative y=(sec(x))/(1+sec(x))	derivative\:y=\frac{\sec(x)}{1+\sec(x)}
integral de 19sin^{-3/2}(x)cos^3(x)	\int\:19\sin^{-\frac{3}{2}}(x)\cos^{3}(x)dx
derivative f(x)=(4-x^2)/(8+x^2)	derivative\:f(x)=\frac{4-x^{2}}{8+x^{2}}
integral de 2x(6x^2-12)^2	\int\:2x(6x^{2}-12)^{2}dx
(\partial)/(\partial x)(e^{xy}+5x-7y+3)	\frac{\partial\:}{\partial\:x}(e^{xy}+5x-7y+3)
límite cuando x tiende a 0-de (-3x^3+4x)/x	\lim\:_{x\to\:0-}(\frac{-3x^{3}+4x}{x})
y^{''}+2y^'-8y=6e^{-2x}-e^{-x}	y^{\prime\:\prime\:}+2y^{\prime\:}-8y=6e^{-2x}-e^{-x}
derivada de (1+sin(x)/(1-sin(x)))	\frac{d}{dx}(\frac{1+\sin(x)}{1-\sin(x)})
laplacetransformación sin(x-5)	laplacetransform\:\sin(x-5)
serie de n=1 a infinity de 3/(nln(9n))	\sum\:_{n=1}^{\infty\:}\frac{3}{n\ln(9n)}
derivative f(x)=(x+(x+sin^2(x))^3)^4	derivative\:f(x)=(x+(x+\sin^{2}(x))^{3})^{4}
integral de x^2cos(21x)	\int\:x^{2}\cos(21x)dx
integral de 0 a 5 de \|3-x\|	\int\:_{0}^{5}\left\|3-x\right\|dx
(\partial)/(\partial x)(y*r^2)	\frac{\partial\:}{\partial\:x}(y\cdot\:r^{2})
integral de (5sqrt(ln(x)))/x	\int\:\frac{5\sqrt{\ln(x)}}{x}dx
y^'=(y-1)(y-1)	y^{\prime\:}=(y-1)(y-1)
integral de 1 a 5 de 2	\int\:_{1}^{5}2dy
xe^{y-x^2}dx-dy=0	xe^{y-x^{2}}dx-dy=0
tangent f(x)=x^2-6,(5,19)	tangent\:f(x)=x^{2}-6,(5,19)
derivada de x^3e^{2x}	\frac{d}{dx}(x^{3}e^{2x})
(\partial)/(\partial x)(4y+9x^2)	\frac{\partial\:}{\partial\:x}(4y+9x^{2})
(dy)/(dx)=sqrt(17x+y)-17	\frac{dy}{dx}=\sqrt{17x+y}-17
derivada de x^{(1/2})	\frac{d}{dx}(x^{(\frac{1}{2})})
derivada de a/(x^2)	\frac{d}{dx}(\frac{a}{x^{2}})
maclaurin 1/((1-x^2))	maclaurin\:\frac{1}{(1-x^{2})}
integral de 1/(sqrt(u^2+4))	\int\:\frac{1}{\sqrt{u^{2}+4}}du
derivative f(x)=(x^2+3)^3*4x^2	derivative\:f(x)=(x^{2}+3)^{3}\cdot\:4x^{2}
límite cuando x tiende a 0 de ((ln(x))^2)/x	\lim\:_{x\to\:0}(\frac{(\ln(x))^{2}}{x})
y^'=(x+y)^2	y^{\prime\:}=(x+y)^{2}
derivative (1+csc(x^3))/(1-cot(x^3))	derivative\:\frac{1+\csc(x^{3})}{1-\cot(x^{3})}
derivada de 24	\frac{d}{dx}(24)
(\partial)/(\partial v)(3u)	\frac{\partial\:}{\partial\:v}(3u)
integral de 0 a pi/4 de 9sec(x)	\int\:_{0}^{\frac{π}{4}}9\sec(x)dx
(dy)/(dx)=(x+y+1)^2-(x+y-1)^2	\frac{dy}{dx}=(x+y+1)^{2}-(x+y-1)^{2}
integral de (x-3)/((x^2+2x+4)^2)	\int\:\frac{x-3}{(x^{2}+2x+4)^{2}}dx

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