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Problemas populares de Cálculo

y^'=x+y,y(0)=4	y^{\prime\:}=x+y,y(0)=4
derivada de ln(cos((x-1/x)))	\frac{d}{dx}(\ln(\cos(\frac{x-1}{x})))
límite cuando x tiende a 0 de x^5*cos(1/x)	\lim\:_{x\to\:0}(x^{5}\cdot\:\cos(\frac{1}{x}))
integral de (1/(x^5))	\int\:(\frac{1}{x^{5}})dx
integral de 1 a 3 de 8^x-2^x	\int\:_{1}^{3}8^{x}-2^{x}dx
pendiente (3,1),(-2,-1)	slope\:(3,1),(-2,-1)
-7y^'+21x^2=0	-7y^{\prime\:}+21x^{2}=0
derivada de 25e^{-5x}	\frac{d}{dx}(25e^{-5x})
integral de (13-6x+21x^6)	\int\:(13-6x+21x^{6})dx
derivada de (cos(2x)/(sin(x)))	\frac{d}{dx}(\frac{\cos(2x)}{\sin(x)})
integral de 1 a 2 de x/(x^2+4x+20)	\int\:_{1}^{2}\frac{x}{x^{2}+4x+20}dx
integral de ((2+x))/(sqrt(4-2x-x^2))	\int\:\frac{(2+x)}{\sqrt{4-2x-x^{2}}}dx
integral de (sin(y)+ysin(x)+1/x)	\int\:(\sin(y)+y\sin(x)+\frac{1}{x})dx
derivada de x^2*sqrt(x)	\frac{d}{dx}(x^{2}\cdot\:\sqrt{x})
inversalaplace s/((s-3)(s-6)(s-2))	inverselaplace\:\frac{s}{(s-3)(s-6)(s-2)}
integral de 0 a 0.4 de ((x^2))/(sqrt(4-25x^2))	\int\:_{0}^{0.4}\frac{(x^{2})}{\sqrt{4-25x^{2}}}dx
integral de (sin(x))(cos(x))	\int\:(\sin(x))(\cos(x))dx
derivada de (x^5-9sqrt(x))	\frac{d}{dx}((x^{5}-9)\sqrt{x})
área x=-3,x=1,y=x^3+1,y=0	area\:x=-3,x=1,y=x^{3}+1,y=0
integral de 2 a infinity de xe^{-2x}	\int\:_{2}^{\infty\:}xe^{-2x}dx
(\partial)/(\partial x)(yx-y-x)	\frac{\partial\:}{\partial\:x}(yx-y-x)
derivada de ((1+tan(x)^2)/(sec(x)))	\frac{d}{dx}(\frac{(1+\tan(x))^{2}}{\sec(x)})
(ln(x/2))^'	(\ln(\frac{x}{2}))^{\prime\:}
y^'=5x-y	y^{\prime\:}=5x-y
integral de 15+(200)/(x+1)	\int\:15+\frac{200}{x+1}dx
d/(dt)(sin(8t))	\frac{d}{dt}(\sin(8t))
derivada de (x/2 ^{2/3})	\frac{d}{dx}((\frac{x}{2})^{\frac{2}{3}})
derivada de xy^2-x^3y	\frac{d}{dx}(xy^{2}-x^{3}y)
integral de x^3(1-x^2)^{3/2}	\int\:x^{3}(1-x^{2})^{\frac{3}{2}}dx
(\partial)/(\partial x)(cos(3x+yz)*3)	\frac{\partial\:}{\partial\:x}(\cos(3x+yz)\cdot\:3)
derivada de ((x-3/(x+4))(x^2+2x+1))	\frac{d}{dx}((\frac{x-3}{x+4})(x^{2}+2x+1))
integral de 0 a 3 de sin^2(mx)	\int\:_{0}^{3}\sin^{2}(mx)dx
derivative 1/(6x-12)sqrt(2x+16)	derivative\:\frac{1}{6x-12}\sqrt{2x+16}
derivada de sqrt(x)+1/(x^3)	\frac{d}{dx}(\sqrt{x}+\frac{1}{x^{3}})
(\partial)/(\partial x)(x^2+y^3)	\frac{\partial\:}{\partial\:x}(x^{2}+y^{3})
normal h(x)=3e^x-7x,(0,3)	normal\:h(x)=3e^{x}-7x,(0,3)
inversalaplace 1/(2s+5)	inverselaplace\:\frac{1}{2s+5}
límite cuando x tiende a+0 de cos^2(x)	\lim\:_{x\to\:+0}(\cos^{2}(x))
límite cuando x tiende a-infinity de-3	\lim\:_{x\to\:-\infty\:}(-3)
(\partial)/(\partial x)(4/3 pi(y^3-x^3))	\frac{\partial\:}{\partial\:x}(\frac{4}{3}π(y^{3}-x^{3}))
paridad x^{6cos(x)}	parity\:x^{6\cos(x)}
derivative e^{-11x}	derivative\:e^{-11x}
derivative (8x^2-5)^{1/2}	derivative\:(8x^{2}-5)^{\frac{1}{2}}
integral de 0 a 3 de (2x-1)	\int\:_{0}^{3}(2x-1)dx
(\partial)/(\partial z)(x^2+(y-1)^2+z^2)	\frac{\partial\:}{\partial\:z}(x^{2}+(y-1)^{2}+z^{2})
derivative f(y)=5x+(135)/x (15x+30)	derivative\:f(y)=5x+\frac{135}{x}(15x+30)
derivada de ((x^2+6/(x^2-6))^4)	\frac{d}{dx}((\frac{x^{2}+6}{x^{2}-6})^{4})
límite cuando x tiende a 2-de (mx-3m)/(x-3)	\lim\:_{x\to\:2-}(\frac{mx-3m}{x-3})
integral de (4e^x)/(e^x+sqrt(3))	\int\:\frac{4e^{x}}{e^{x}+\sqrt{3}}dx
derivada de x^{4/5}(x-4^2)	\frac{d}{dx}(x^{\frac{4}{5}}(x-4)^{2})
xy+y^2-x^2(dy)/(dx)=0	xy+y^{2}-x^{2}\frac{dy}{dx}=0
integral de 1 a 2 de 11sqrt(4x^2-3)	\int\:_{1}^{2}11\sqrt{4x^{2}-3}dx
inversalaplace 1/((s^2+1)(s^2-6))	inverselaplace\:\frac{1}{(s^{2}+1)(s^{2}-6)}
f(x)=(e^x+1)^{7x}	f(x)=(e^{x}+1)^{7x}
inversalaplace 4/s+6/(s^2)-1/(s+8)	inverselaplace\:\frac{4}{s}+\frac{6}{s^{2}}-\frac{1}{s+8}
derivada de (cos(xe^x)/(tan(x)))	\frac{d}{dx}(\frac{\cos(x)e^{x}}{\tan(x)})
y^{'''}+8y^{''}-12y^'-144y=0	y^{\prime\:\prime\:\prime\:}+8y^{\prime\:\prime\:}-12y^{\prime\:}-144y=0
derivada de sin(pi{f}(x))	\frac{d}{dx}(\sin(π{f}(x)))
derivative ln(x+8)	derivative\:\ln(x+8)
integral de 0 a 2 de sqrt(x+1)	\int\:_{0}^{2}\sqrt{x+1}dx
derivada de e^{x^2+3x}	\frac{d}{dx}(e^{x^{2}+3x})
extreme f(x)=sqrt(r^2-14x^2)	extreme\:f(x)=\sqrt{r^{2}-14x^{2}}
derivada de ax+b	\frac{d}{dx}(ax+b)
derivada de (-2cos(2x-sin(3x)-3)^2)	\frac{d}{dx}((-2\cos(2x)-\sin(3x)-3)^{2})
integral de x^{-n}	\int\:x^{-n}dx
derivative y=(2log_{e}(x)-3)^4	derivative\:y=(2\log_{e}(x)-3)^{4}
integral de ((7x+29))/(x^2+8x+15)	\int\:\frac{(7x+29)}{x^{2}+8x+15}dx
derivative x^{9/5}	derivative\:x^{\frac{9}{5}}
laplacetransformación 3(t-2)^2+10(t-2)+9	laplacetransform\:3(t-2)^{2}+10(t-2)+9
integral de ((x^2+1)^3)/x	\int\:\frac{(x^{2}+1)^{3}}{x}dx
integral de (4x^2)/3	\int\:\frac{4x^{2}}{3}dx
integral de (x-3)/(sqrt(x^2-4x+5))	\int\:\frac{x-3}{\sqrt{x^{2}-4x+5}}dx
límite cuando x tiende a-1 de 2x-1	\lim\:_{x\to\:-1}(2x-1)
derivative sqrt(1+x^3)	derivative\:\sqrt{1+x^{3}}
límite cuando x tiende a x de (sin(x))/x	\lim\:_{x\to\:x}(\frac{\sin(x)}{x})
integral de 0 a infinity de 1/(x^4)	\int\:_{0}^{\infty\:}\frac{1}{x^{4}}dx
límite cuando x tiende a 0 de 2x-1/(x^2)	\lim\:_{x\to\:0}(2x-\frac{1}{x^{2}})
inversalaplace 1/((s-2)(s+1)(s-3))	inverselaplace\:\frac{1}{(s-2)(s+1)(s-3)}
derivada de x^3+3x+2	\frac{d}{dx}(x^{3}+3x+2)
integral de x/(3x^2+2)	\int\:\frac{x}{3x^{2}+2}dx
derivative 6e^{6e^x+x}	derivative\:6e^{6e^{x}+x}
derivative (x^3+7)e^x	derivative\:(x^{3}+7)e^{x}
derivative f(x)=-1x^{-3/5}	derivative\:f(x)=-1x^{-\frac{3}{5}}
derivada de cos(x/y)	\frac{d}{dx}(\cos(\frac{x}{y}))
d/(da)(2sin(2a)+2cos^2(a))	\frac{d}{da}(2\sin(2a)+2\cos^{2}(a))
inversalaplace 2/(s+1)+(16s)/(s^2+9)	inverselaplace\:\frac{2}{s+1}+\frac{16s}{s^{2}+9}
pendiente (1.4)(3.5)	slope\:(1.4)(3.5)
inversalaplace 1/(s^2+3s)	inverselaplace\:\frac{1}{s^{2}+3s}
derivada de (2x^8)	\frac{d}{dx}((2x)^{8})
límite cuando x tiende a 0+de 6-ln(x)	\lim\:_{x\to\:0+}(6-\ln(x))
serie de n=3 a infinity de 1/(n+2)	\sum\:_{n=3}^{\infty\:}\frac{1}{n+2}
y^'(x)=(3x^2)/(3y^2-7),y(1)=0	y^{\prime\:}(x)=\frac{3x^{2}}{3y^{2}-7},y(1)=0
tangent f(x)=sqrt(3x+4),(7,5)	tangent\:f(x)=\sqrt{3x+4},(7,5)
(\partial)/(\partial x)(0.1y^2+0.05x*y)	\frac{\partial\:}{\partial\:x}(0.1\cdot\:y^{2}+0.05\cdot\:x\cdot\:y)
integral de (sec(x))	\int\:(\sec(x))dx
derivada de arcsin(6x)	\frac{d}{dx}(\arcsin(6x))
derivada de 3arcsinh(tan(x))	\frac{d}{dx}(3\arcsinh(\tan(x)))
derivative cos(-5x)	derivative\:\cos(-5x)
integral de sec^3(1)	\int\:\sec^{3}(1)dx
integral de sqrt(1-3x^2)	\int\:\sqrt{1-3x^{2}}dx

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