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Popular Calculus Problems

laplacetransform g(t)=4cos(4t)-9sin(4t)+2cos(10t)	laplacetransform\:g(t)=4\cos(4t)-9\sin(4t)+2\cos(10t)
(\partial)/(\partial x)(rsin(t)sin(x))	\frac{\partial\:}{\partial\:x}(r\sin(t)\sin(x))
(\partial)/(\partial x)(e^{-(x^2+y^2+2z^2)})	\frac{\partial\:}{\partial\:x}(e^{-(x^{2}+y^{2}+2z^{2})})
integral of (10+u)/u	\int\:\frac{10+u}{u}du
integral of 3/(sqrt(x))+(xsqrt(x))/4+C	\int\:\frac{3}{\sqrt{x}}+\frac{x\sqrt{x}}{4}+Cdx
d/(dt)(10000-9000e^{-0.3t})	\frac{d}{dt}(10000-9000e^{-0.3t})
integral of (x-1)/(x^2-x-1)	\int\:\frac{x-1}{x^{2}-x-1}dx
(\partial)/(\partial y)(7xy^6)	\frac{\partial\:}{\partial\:y}(7xy^{6})
tangent of 3x^3-6x^2+4x+21	tangent\:3x^{3}-6x^{2}+4x+21
integral of (7x+3)/((x+4)(x-1))	\int\:\frac{7x+3}{(x+4)(x-1)}dx
limit as x approaches 1 of (1/x-1)/(1-x)	\lim\:_{x\to\:1}(\frac{\frac{1}{x}-1}{1-x})
limit as x approaches 0 of (18)/(x^2)	\lim\:_{x\to\:0}(\frac{18}{x^{2}})
derivative of 9/((x-8^2))	\frac{d}{dx}(\frac{9}{(x-8)^{2}})
(\partial)/(\partial x)(3x^2-24y)	\frac{\partial\:}{\partial\:x}(3x^{2}-24y)
derivative of-2ln(x)	\frac{d}{dx}(-2\ln(x))
derivative of (x-2^3(x-6))	\frac{d}{dx}((x-2)^{3}(x-6))
area 5x, 5/x ,x=5	area\:5x,\frac{5}{x},x=5
derivative of (x-1^{1/3}(x+2)^{2/3})	\frac{d}{dx}((x-1)^{\frac{1}{3}}(x+2)^{\frac{2}{3}})
derivative of e^{13t}cos(t)	derivative\:e^{13t}\cos(t)
(dy}{dx}+\frac{x^2)/y =0	\frac{dy}{dx}+\frac{x^{2}}{y}=0
limit as x approaches 0 of x^{21x}	\lim\:_{x\to\:0}(x^{21x})
derivative of y=x^2+4x-3	derivative\:y=x^{2}+4x-3
integral of sin(16x)cos(11x)	\int\:\sin(16x)\cos(11x)dx
(dN)/(dt)=5-N	\frac{dN}{dt}=5-N
derivative of (2x+x^2)/((1+x)^2)	derivative\:\frac{2x+x^{2}}{(1+x)^{2}}
(dy)/(dx)=(x-y)/(x+2y)	\frac{dy}{dx}=\frac{x-y}{x+2y}
(9+x)(dy)/(dx)=6+x	(9+x)\frac{dy}{dx}=6+x
derivative of (xy/2)	\frac{d}{dx}(\frac{xy}{2})
(\partial)/(\partial y)(-20xy^2+6x)	\frac{\partial\:}{\partial\:y}(-20xy^{2}+6x)
xy^'=y^2,y(1)=1	xy^{\prime\:}=y^{2},y(1)=1
ty^'-3y=t^4	t\cdot\:y^{\prime\:}-3\cdot\:y=t^{4}
laplacetransform (t+2)^2e^t	laplacetransform\:(t+2)^{2}e^{t}
laplacetransform t*e^{-t}	laplacetransform\:t\cdot\:e^{-t}
f(x)=x^3e^x	f(x)=x^{3}e^{x}
integral of 1/(2x^2-4x+12)	\int\:\frac{1}{2x^{2}-4x+12}dx
derivative of x^3+y^2	\frac{d}{dx}(x^{3}+y^{2})
integral of ye^{-y^2}	\int\:ye^{-y^{2}}dy
tangent of y=-3-7x^2	tangent\:y=-3-7x^{2}
derivative of 3^{4x^2+3x}	\frac{d}{dx}(3^{4x^{2}+3x})
(\partial)/(\partial x)(2e^{x^2})	\frac{\partial\:}{\partial\:x}(2e^{x^{2}})
limit as x approaches 0 of (14)/x	\lim\:_{x\to\:0}(\frac{14}{x})
f^'(x)=6sqrt(x)-\sqrt[6]{x}	f^{\prime\:}(x)=6\sqrt{x}-\sqrt[6]{x}
inverse oflaplace (10)/((s*(s+1)))	inverselaplace\:\frac{10}{(s\cdot\:(s+1))}
area x^2-2x,4x+7	area\:x^{2}-2x,4x+7
((x^2-1)dy)/(dx)+3x(y-1)=0,y(0)=7	\frac{(x^{2}-1)dy}{dx}+3x(y-1)=0,y(0)=7
tangent of ((2x-1)/(x+1)),2	tangent\:(\frac{2x-1}{x+1}),2
integral of 8arctan(sqrt(x))	\int\:8\arctan(\sqrt{x})dx
limit as z approaches 2 of (-2/(z+2))^3	\lim\:_{z\to\:2}((-\frac{2}{z+2})^{3})
(dy)/(dx)=e^{2x}+3y	\frac{dy}{dx}=e^{2x}+3y
integral of xsqrt(16+x^2)	\int\:x\sqrt{16+x^{2}}dx
f(x)=ln(1+1/x)	f(x)=\ln(1+\frac{1}{x})
derivative of 3xsin(pix)	\frac{d}{dx}(3x\sin(πx))
(x/(sqrt(x^2+1)))^'	(\frac{x}{\sqrt{x^{2}+1}})^{\prime\:}
derivative of x/(sqrt(x^2+8))	derivative\:\frac{x}{\sqrt{x^{2}+8}}
integral from-infinity to 2 of xe^x	\int\:_{-\infty\:}^{2}xe^{x}dx
laplacetransform s+2	laplacetransform\:s+2
derivative of 6x^2y-3xy^2	\frac{d}{dx}(6x^{2}y-3xy^{2})
integral of (5x^3)	\int\:(5x^{3})dx
tangent of f(x)=-6/((3x+5)^2),\at x=-1	tangent\:f(x)=-\frac{6}{(3x+5)^{2}},\at\:x=-1
tangent of f(x)=x^2-1	tangent\:f(x)=x^{2}-1
integral of (x^3)/(x^4-2)	\int\:\frac{x^{3}}{x^{4}-2}dx
derivative of g(w)=12\sqrt[3]{w}	derivative\:g(w)=12\sqrt[3]{w}
derivative of f(x)= 1/(sqrt(x-2))	derivative\:f(x)=\frac{1}{\sqrt{x-2}}
(\partial)/(\partial x)((-4x^5)/(4y^4))	\frac{\partial\:}{\partial\:x}(\frac{-4x^{5}}{4y^{4}})
(dy)/(dx)y=sqrt(x)	\frac{dy}{dx}y=\sqrt{x}
tangent of-x^2+3x+7	tangent\:-x^{2}+3x+7
d/(d{y)}(({y})/({z)})	\frac{d}{d{y}}(\frac{{y}}{{z}})
integral of 1/(x^2+4x+68)	\int\:\frac{1}{x^{2}+4x+68}dx
(\partial)/(\partial x)(arctan(x/y))	\frac{\partial\:}{\partial\:x}(\arctan(\frac{x}{y}))
derivative of 4x^3-12x	\frac{d}{dx}(4x^{3}-12x)
integral from 3 to 5 of (2x^2+x+4)/(x-1)	\int\:_{3}^{5}\frac{2x^{2}+x+4}{x-1}dx
integral from 1 to e of ((1+ln(x))^2)/x	\int\:_{1}^{e}\frac{(1+\ln(x))^{2}}{x}dx
integral of (tan(ln(x)))/x	\int\:\frac{\tan(\ln(x))}{x}dx
derivative of (3x^3+x^{-3})(x+3)(x^2-5)	derivative\:(3x^{3}+x^{-3})(x+3)(x^{2}-5)
f^'(x)=2x^3-x	f^{\prime\:}(x)=2x^{3}-x
derivative of y=ce^{(-x^3)/3}+1	derivative\:y=ce^{\frac{-x^{3}}{3}}+1
integral from 1 to 5 of 6250pix	\int\:_{1}^{5}6250πxdx
derivative of f(x)=x^3+x	derivative\:f(x)=x^{3}+x
tangent of 2sqrt(x),\at x=9	tangent\:2\sqrt{x},\at\:x=9
tangent of f(x)=(8x)/(x^2-1),\at x=3	tangent\:f(x)=\frac{8x}{x^{2}-1},\at\:x=3
derivative of ((6x^2)/(8-x))^3	derivative\:(\frac{6x^{2}}{8-x})^{3}
derivative of x^{-5}	derivative\:x^{-5}
integral of 4sin(5x)	\int\:4\sin(5x)dx
integral of 1/(x^{2/3)(8+x^{1/3})}	\int\:\frac{1}{x^{\frac{2}{3}}(8+x^{\frac{1}{3}})}dx
derivative of y(θ)=ln(θ+1)-e^θ	derivative\:y(θ)=\ln(θ+1)-e^{θ}
(\partial)/(\partial x)(ln(x+y)-5y)	\frac{\partial\:}{\partial\:x}(\ln(x+y)-5y)
derivative of (x+3^x)	\frac{d}{dx}((x+3)^{x})
derivative of x^{5e^x}	\frac{d}{dx}(x^{5e^{x}})
area ln(x/2-3),[7,9]	area\:\ln(\frac{x}{2}-3),[7,9]
integral from 0 to 3 of integral from 0 to y of e^{-y^2}	\int\:_{0}^{3}\int\:_{0}^{y}e^{-y^{2}}dxdy
integral of x^2+3x+C	\int\:x^{2}+3x+Cdx
sum from n=0 to infinity of n(6/7)^n	\sum\:_{n=0}^{\infty\:}n(\frac{6}{7})^{n}
integral of 2000(x-4)e^{x^2-8x}	\int\:2000(x-4)e^{x^{2}-8x}dx
slope of 2x^2-4	slope\:2x^{2}-4
f(x)=x^3+2	f(x)=x^{3}+2
sum from n=1 to infinity of 17^nx^nn!	\sum\:_{n=1}^{\infty\:}17^{n}x^{n}n!
(dy)/(dx)=3x^2(y^2+1)	\frac{dy}{dx}=3x^{2}(y^{2}+1)
derivative of x-10	\frac{d}{dx}(x-10)
tangent of y=6e^xcos(x),(0,6)	tangent\:y=6e^{x}\cos(x),(0,6)
sum from n=1 to infinity of pi^{-n}	\sum\:_{n=1}^{\infty\:}π^{-n}

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