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Popular Calculus Problems

limit as x approaches 0+of (x^2e^{1/x})/(1+x^2)	\lim\:_{x\to\:0+}(\frac{x^{2}e^{\frac{1}{x}}}{1+x^{2}})
y^'=sqrt((x+3)/(y+8))	y^{\prime\:}=\sqrt{\frac{x+3}{y+8}}
derivative of f(x)=x^2-9x+118	derivative\:f(x)=x^{2}-9x+118
derivative of x^{(-1/2}sin(x))	\frac{d}{dx}(x^{\frac{-1}{2}}\sin(x))
integral of 3(3x+2)	\int\:3(3x+2)dx
integral of 1/((1-2x))	\int\:\frac{1}{(1-2x)}dx
limit as x approaches 2pi-of xcsc(x)	\lim\:_{x\to\:2π-}(x\csc(x))
derivative of 5x^2+4	\frac{d}{dx}(5x^{2}+4)
limit as x approaches-5 of \|x+5\|	\lim\:_{x\to\:-5}(\left\|x+5\right\|)
(\partial)/(\partial x)(x^{1/2}y)	\frac{\partial\:}{\partial\:x}(x^{\frac{1}{2}}y)
(dy)/(dx)=3+2-5y	\frac{dy}{dx}=3+2-5y
derivative of ((qx+r(q,x,t))/(sx+t))	\frac{d}{dx}(\frac{(qx+r(q,x,t))}{sx+t})
(dy)/(dx)=(x+y)/(2x)	\frac{dy}{dx}=\frac{x+y}{2x}
(\partial)/(\partial x)(((e^y))/(x+y^4))	\frac{\partial\:}{\partial\:x}(\frac{(e^{y})}{x+y^{4}})
limit as x approaches-1 of x^2-4	\lim\:_{x\to\:-1}(x^{2}-4)
derivative of (x+6/(sqrt(x^2+6)))	\frac{d}{dx}(\frac{x+6}{\sqrt{x^{2}+6}})
derivative of sqrt(3x^2-5x+6)	\frac{d}{dx}(\sqrt{3x^{2}-5x+6})
(dy)/(dx)=-8y	\frac{dy}{dx}=-8y
integral of 17x^{16}	\int\:17x^{16}dx
derivative of f(x)=-3x+1	derivative\:f(x)=-3x+1
integral of (3x)/(sqrt(3-x^2))	\int\:\frac{3x}{\sqrt{3-x^{2}}}dx
derivative of f(x)=-5x+2	derivative\:f(x)=-5x+2
(dy)/(dx)+4y=8	\frac{dy}{dx}+4y=8
integral of 9/(x^3-3x^2)	\int\:\frac{9}{x^{3}-3x^{2}}dx
y^'+5y=cos(x)	y^{\prime\:}+5y=\cos(x)
integral of 3xsec^2(4x^2)	\int\:3x\sec^{2}(4x^{2})dx
integral of e^x+x^2+x^3	\int\:e^{x}+x^{2}+x^{3}dx
integral from 0 to 1 of te^{-st}	\int\:_{0}^{1}te^{-st}dt
derivative of 60x^4+180x^3-240x^2	\frac{d}{dx}(60x^{4}+180x^{3}-240x^{2})
derivative of f(x)=(-2x^2-4)^3	derivative\:f(x)=(-2x^{2}-4)^{3}
inverse oflaplace 1/(1+s)	inverselaplace\:\frac{1}{1+s}
derivative of (arcsin(x)/x)	\frac{d}{dx}(\frac{\arcsin(x)}{x})
(\partial)/(\partial x)(x^2y+4y)	\frac{\partial\:}{\partial\:x}(x^{2}y+4y)
integral of (-5x)/((x^2+5)^{3/2)}	\int\:\frac{-5x}{(x^{2}+5)^{\frac{3}{2}}}dx
derivative of y=xln(sin^2(x))	derivative\:y=x\ln(\sin^{2}(x))
y(x+7)+(dy)/(dx)=0	y(x+7)+\frac{dy}{dx}=0
integral of (-1)/(sqrt(1/4-x^2))	\int\:\frac{-1}{\sqrt{\frac{1}{4}-x^{2}}}dx
(e^t(5-3e^{-2t}))^'	(e^{t}(5-3e^{-2t}))^{\prime\:}
integral of 12x^3	\int\:12x^{3}dx
laplacetransform 250	laplacetransform\:250
limit as x approaches 0 of sqrt(x+1)	\lim\:_{x\to\:0}(\sqrt{x+1})
limit as x approaches 0 of ((e^x-1))/x	\lim\:_{x\to\:0}(\frac{(e^{x}-1)}{x})
integral of (4x^3-3x^2+6x-1)	\int\:(4x^{3}-3x^{2}+6x-1)dx
limit as x approaches 0 of sin(x)ln(2x)	\lim\:_{x\to\:0}(\sin(x)\ln(2x))
1/(1+u^2)du=dx	\frac{1}{1+u^{2}}du=dx
derivative of (\sqrt[7]{x}/6)	\frac{d}{dx}(\frac{\sqrt[7]{x}}{6})
(\partial)/(\partial x)(6e^{x^5y^3})	\frac{\partial\:}{\partial\:x}(6e^{x^{5}y^{3}})
integral of 10x^3y	\int\:10x^{3}ydy
derivative of y=((x))/(sqrt(x^2+1))	derivative\:y=\frac{(x)}{\sqrt{x^{2}+1}}
tangent of \sqrt[5]{x}	tangent\:\sqrt[5]{x}
slope of f(x)=x^4-17x^2+16	slope\:f(x)=x^{4}-17x^{2}+16
integral from 0 to 1 of x^2-x^3	\int\:_{0}^{1}x^{2}-x^{3}dx
tangent of f(x)=2x^2+1,(-1,3)	tangent\:f(x)=2x^{2}+1,(-1,3)
derivative of f(x)=(e^x)/(9x^2+2)	derivative\:f(x)=\frac{e^{x}}{9x^{2}+2}
integral of 1/(u^2)	\int\:\frac{1}{u^{2}}du
integral of 4e^{-3x}	\int\:4e^{-3x}dx
derivative of x^{1/8}	\frac{d}{dx}(x^{\frac{1}{8}})
f(x)= x/6	f(x)=\frac{x}{6}
tangent of f(x)=(6x^2-1)/(-3x+1),\at x=0	tangent\:f(x)=\frac{6x^{2}-1}{-3x+1},\at\:x=0
integral from 2 to 4 of 1/(sqrt(16-x^2))	\int\:_{2}^{4}\frac{1}{\sqrt{16-x^{2}}}dx
(\partial)/(\partial y)(e^{x^2})	\frac{\partial\:}{\partial\:y}(e^{x^{2}})
integral of 4x^{-5}	\int\:4x^{-5}dx
integral of (x-1)e^{-x-1}	\int\:(x-1)e^{-x-1}dx
sum from n=0 to infinity of e	\sum\:_{n=0}^{\infty\:}e
derivative of f(x)=sqrt(x)-1/x	derivative\:f(x)=\sqrt{x}-\frac{1}{x}
derivative of (-1/((x-2)^2))	\frac{d}{dx}(\frac{-1}{(x-2)^{2}})
limit as x approaches-infinity of e^x+e^{-x}	\lim\:_{x\to\:-\infty\:}(e^{x}+e^{-x})
integral of 16-8x^2+x^4	\int\:16-8x^{2}+x^{4}dx
integral of \sqrt[a]{x^2}	\int\:\sqrt[a]{x^{2}}dx
f(x)=(tan(x)-1)/(sec(x))	f(x)=\frac{\tan(x)-1}{\sec(x)}
2x^2y^'=piysin(pi/(2x))	2x^{2}y^{\prime\:}=πy\sin(\frac{π}{2x})
derivative of x^{6cos(x)}	derivative\:x^{6\cos(x)}
derivative of 8^{x^4}	\frac{d}{dx}(8^{x^{4}})
area x/(1+x^2),(x^2)/(1+x^3),[0,1]	area\:\frac{x}{1+x^{2}},\frac{x^{2}}{1+x^{3}},[0,1]
integral of 8/(4+8x)	\int\:\frac{8}{4+8x}dx
derivative of (180)/(x^7)-4/(x^3)	derivative\:\frac{180}{x^{7}}-\frac{4}{x^{3}}
(dy)/(dx)=(e^x-e^{-x})^2	\frac{dy}{dx}=(e^{x}-e^{-x})^{2}
tangent of f(x)=x^2,(0,-9)	tangent\:f(x)=x^{2},(0,-9)
derivative of sin(θ)+cos(θ)	derivative\:\sin(θ)+\cos(θ)
derivative of 2sec(xtan(x))	\frac{d}{dx}(2\sec(x)\tan(x))
taylor arctan(x),0	taylor\:\arctan(x),0
integral of (e^{cos(x)})/(csc(x))	\int\:\frac{e^{\cos(x)}}{\csc(x)}dx
yy^'=-t	yy^{\prime\:}=-t
y^{''}+2y^'+17y=0,y(0)=3,y^'(0)=0	y^{\prime\:\prime\:}+2y^{\prime\:}+17y=0,y(0)=3,y^{\prime\:}(0)=0
limit as x approaches 2 of ln(4-2x)	\lim\:_{x\to\:2}(\ln(4-2x))
integral of sqrt(1+x^2)x	\int\:\sqrt{1+x^{2}}xdx
derivative of-2x-3x^5	\frac{d}{dx}(-2x-3x^{5})
derivative of (4x+9/(sqrt(x)))	\frac{d}{dx}(\frac{4x+9}{\sqrt{x}})
derivative of ((x^2-1)^3)/(x^2+4)	derivative\:\frac{(x^{2}-1)^{3}}{x^{2}+4}
integral of 3x^2-6x+3	\int\:3x^{2}-6x+3dx
integral of (x-1)/(x+1)	\int\:\frac{x-1}{x+1}dx
derivative of 2(x^2+5x-2^{-5/7})	\frac{d}{dx}(2(x^{2}+5x-2)^{-\frac{5}{7}})
(d^2y)/(dt^2)+9y=0	\frac{d^{2}y}{dt^{2}}+9y=0
derivative of csc^2(x-2)	\frac{d}{dx}(\csc^{2}(x-2))
integral from 0 to 1 of x(1-x)^5	\int\:_{0}^{1}x(1-x)^{5}dx
(\partial)/(\partial x)(x^{0.4}y^{0.6})	\frac{\partial\:}{\partial\:x}(x^{0.4}y^{0.6})
derivative of sqrt(1+2e^{3x)}	\frac{d}{dx}(\sqrt{1+2e^{3x}})
integral of 16cot^4(x)	\int\:16\cot^{4}(x)dx
integral of ((x+1))/(x^3+x^2-6x)	\int\:\frac{(x+1)}{x^{3}+x^{2}-6x}dx
integral from 3 to 4 of x/(x-3)	\int\:_{3}^{4}\frac{x}{x-3}dx

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