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Popular Calculus Problems

(\partial)/(\partial x)(x^3-3xy+y^3)	\frac{\partial\:}{\partial\:x}(x^{3}-3xy+y^{3})
limit as x approaches-2 of 1/(\|x+2\|)+x^2	\lim\:_{x\to\:-2}(\frac{1}{\left\|x+2\right\|}+x^{2})
y^'=2.5-y/(2000)	y^{\prime\:}=2.5-\frac{y}{2000}
(dy)/(dt)+1/2 y=17sin(2t),y(0)=-1	\frac{dy}{dt}+\frac{1}{2}y=17\sin(2t),y(0)=-1
integral of x^{-2}+x^{1/5}	\int\:x^{-2}+x^{\frac{1}{5}}dx
derivative of arctan(sx)	\frac{d}{dx}(\arctan(sx))
derivative of tan(x-y)	\frac{d}{dx}(\tan(x-y))
integral of \sqrt[9]{r^2}	\int\:\sqrt[9]{r^{2}}dr
laplacetransform 3cos(8t)	laplacetransform\:3\cos(8t)
y^{''}-2y-8y=0,y(0)=-2,y^'(0)=4	y^{\prime\:\prime\:}-2y-8y=0,y(0)=-2,y^{\prime\:}(0)=4
integral of e^{3x+e^x}	\int\:e^{3x+e^{x}}dx
laplacetransform 6(t-10)	laplacetransform\:6(t-10)
derivative of f(x)=(11x)/(1-x)	derivative\:f(x)=\frac{11x}{1-x}
derivative of log_{4}(x^2)	derivative\:\log_{4}(x^{2})
(\partial)/(\partial x)(1/(\sqrt[3]{x)})	\frac{\partial\:}{\partial\:x}(\frac{1}{\sqrt[3]{x}})
limit as x approaches infinity of 7+2/x	\lim\:_{x\to\:\infty\:}(7+\frac{2}{x})
slope of (-6,4),(-11,-1)	slope\:(-6,4),(-11,-1)
y^'=2y(1-y)	y^{\prime\:}=2y(1-y)
(\partial)/(\partial x)(((2x+2y))/(-6x-8y))	\frac{\partial\:}{\partial\:x}(\frac{(2x+2y)}{-6x-8y})
limit as x approaches 3+of \|x-3\|	\lim\:_{x\to\:3+}(\left\|x-3\right\|)
integral of 9/(1-cos^2(x))	\int\:\frac{9}{1-\cos^{2}(x)}dx
derivative of 3x^2-18x+15	\frac{d}{dx}(3x^{2}-18x+15)
inverse oflaplace (4s)/(s^2+9)	inverselaplace\:\frac{4s}{s^{2}+9}
d/(dy)((1/(y^2)-9/(y^4))(y+7y^3))	\frac{d}{dy}((\frac{1}{y^{2}}-\frac{9}{y^{4}})(y+7y^{3}))
(\partial)/(\partial x)(ln(xe^{-6x}))	\frac{\partial\:}{\partial\:x}(\ln(xe^{-6x}))
limit as x approaches+0 of (1/(x^2))^2	\lim\:_{x\to\:+0}((\frac{1}{x^{2}})^{2})
limit as n approaches-infinity of e^n	\lim\:_{n\to\:-\infty\:}(e^{n})
sum from n=0 to infinity of e^{2n}	\sum\:_{n=0}^{\infty\:}e^{2n}
limit as x approaches 0 of (6^x-2^x)/x	\lim\:_{x\to\:0}(\frac{6^{x}-2^{x}}{x})
limit as x approaches 0+of x^3ln(x)	\lim\:_{x\to\:0+}(x^{3}\ln(x))
tangent of f(x)= x/(x^2+9)	tangent\:f(x)=\frac{x}{x^{2}+9}
x(x+y)y^'+y(3x+y)=0	x(x+y)y^{\prime\:}+y(3x+y)=0
integral of 5cos(3z)+2/(e^{4z)}	\int\:5\cos(3z)+\frac{2}{e^{4z}}dz
2ty^'+y=e^t	2ty^{\prime\:}+y=e^{t}
(\partial)/(\partial y)(x^2-x-12y+1)	\frac{\partial\:}{\partial\:y}(x^{2}-x-12y+1)
integral from 0 to 27 of 4/(x^{2/3)}	\int\:_{0}^{27}\frac{4}{x^{\frac{2}{3}}}dx
integral of 5xln(4x)	\int\:5x\ln(4x)dx
derivative of f(x)=x^2+3x-7	derivative\:f(x)=x^{2}+3x-7
(\partial)/(\partial s)(-3sqrt(s^2+t^2))	\frac{\partial\:}{\partial\:s}(-3\sqrt{s^{2}+t^{2}})
y^'=y+3	y^{\prime\:}=y+3
integral of 1/(sqrt(x^2+6x))	\int\:\frac{1}{\sqrt{x^{2}+6x}}dx
derivative of e^{1x}	\frac{d}{dx}(e^{1x})
derivative of f(x)=sqrt(7)x-sqrt(2x)	derivative\:f(x)=\sqrt{7}x-\sqrt{2x}
integral of (2x^2)/(2x+1)	\int\:\frac{2x^{2}}{2x+1}dx
integral of (2x)/(1+2x)	\int\:\frac{2x}{1+2x}dx
derivative of (x+1/(x-2))	\frac{d}{dx}(\frac{x+1}{x-2})
(dy)/(dx)=sqrt(7y)e^{x+2}	\frac{dy}{dx}=\sqrt{7y}e^{x+2}
(\partial)/(\partial x)((x^2+2)(x^3+1))	\frac{\partial\:}{\partial\:x}((x^{2}+2)(x^{3}+1))
limit as x approaches-5+of (-1)/(x^2-25)	\lim\:_{x\to\:-5+}(\frac{-1}{x^{2}-25})
derivative of sqrt({g)(x}*(ax^2+x))	\frac{d}{dx}(\sqrt{{g}(x)}\cdot\:(ax^{2}+x))
sum from n=2 to infinity}((3^{3n of))/(2^{2n-2)}	\sum\:_{n=2}^{\infty\:}\frac{(3^{3n})}{2^{2n-2}}
limit as x approaches 10 of x/(x^2-100)	\lim\:_{x\to\:10}(\frac{x}{x^{2}-100})
derivative of (-x^2-2/((x^2-2)^2))	\frac{d}{dx}(\frac{-x^{2}-2}{(x^{2}-2)^{2}})
derivative of (1-cos(x)/x)	\frac{d}{dx}(\frac{1-\cos(x)}{x})
integral of (2x-1)/(2x+3)	\int\:\frac{2x-1}{2x+3}dx
d/(d{x)}(ln({x}+2{y}+3{z}))	\frac{d}{d{x}}(\ln({x}+2{y}+3{z}))
y^{'''}=e^{-0.2x}	y^{\prime\:\prime\:\prime\:}=e^{-0.2x}
inverse oflaplace ((s+2))/((s^2+4))	inverselaplace\:\frac{(s+2)}{(s^{2}+4)}
derivative of (x^2+4)(2x-6)	derivative\:(x^{2}+4)(2x-6)
taylor 1/((1+x)^2)	taylor\:\frac{1}{(1+x)^{2}}
integral of x^5cos(x^2)	\int\:x^{5}\cos(x^{2})dx
limit as x approaches 1-of 7/(1-x)	\lim\:_{x\to\:1-}(\frac{7}{1-x})
integral of x/(sqrt(1-4x^2))	\int\:\frac{x}{\sqrt{1-4x^{2}}}dx
integral of (5x)/((7-x^2)^3)	\int\:\frac{5x}{(7-x^{2})^{3}}dx
sum from n=1 to infinity of 1/(n^{1.5)}	\sum\:_{n=1}^{\infty\:}\frac{1}{n^{1.5}}
limit as x approaches 0 of (3x^4-8x)/x	\lim\:_{x\to\:0}(\frac{3x^{4}-8x}{x})
derivative of-75cos(5x)	\frac{d}{dx}(-75\cos(5x))
integral of (x^2)/(2x^2+2)	\int\:\frac{x^{2}}{2x^{2}+2}dx
integral of 9arcsin(x)	\int\:9\arcsin(x)dx
derivative of x^{(4/5}(x-4)^2)	\frac{d}{dx}(x^{(\frac{4}{5})}(x-4)^{2})
(dy)/(dx)= x/(4+x^2)	\frac{dy}{dx}=\frac{x}{4+x^{2}}
derivative of 2^xln(x)	\frac{d}{dx}(2^{x}\ln(x))
integral of (x^2)/(sqrt(x^3+1))	\int\:\frac{x^{2}}{\sqrt{x^{3}+1}}dx
f(x)=e^{x^2+1}	f(x)=e^{x^{2}+1}
derivative of f(x)=10^{sqrt(x)}	derivative\:f(x)=10^{\sqrt{x}}
derivative of (2x/(x^2+4))	\frac{d}{dx}(\frac{2x}{x^{2}+4})
y^'=(3x-2)^2(5x+4)	y^{\prime\:}=(3x-2)^{2}(5x+4)
derivative of t^3-12t	derivative\:t^{3}-12t
y^{''}= 1/(x^2)y	y^{\prime\:\prime\:}=\frac{1}{x^{2}}y
integral from 0 to x of sin(t)	\int\:_{0}^{x}\sin(t)dt
integral from 1 to 3 of (x^2-1)	\int\:_{1}^{3}(x^{2}-1)dx
integral from 1 to 100 of 1/(1+x^2)	\int\:_{1}^{100}\frac{1}{1+x^{2}}dx
area 4x^2,25	area\:4x^{2},25
(\partial)/(\partial x)(x^2+2xy+y^2)	\frac{\partial\:}{\partial\:x}(x^{2}+2xy+y^{2})
derivative of log_{x}(3)	\frac{d}{dx}(\log_{x}(3))
(x^2-4)(dy)/(dx)+2xy=3x^2	(x^{2}-4)\frac{dy}{dx}+2xy=3x^{2}
inverse oflaplace 1/((s^2+4)^2)	inverselaplace\:\frac{1}{(s^{2}+4)^{2}}
d/(dt)(5t^{-3})	\frac{d}{dt}(5t^{-3})
integral from-1 to 1 of e^y-y^2+2	\int\:_{-1}^{1}e^{y}-y^{2}+2dy
(\partial)/(\partial y)(tan(3x-2y+1))	\frac{\partial\:}{\partial\:y}(\tan(3x-2y+1))
inverse oflaplace (s+7)/(s^2+8s+25)	inverselaplace\:\frac{s+7}{s^{2}+8s+25}
derivative of g(x)=(3-4x)^3	derivative\:g(x)=(3-4x)^{3}
limit as x approaches 1-of (2x)/(ln(x))	\lim\:_{x\to\:1-}(\frac{2x}{\ln(x)})
integral of (6x+5)	\int\:(6x+5)dx
integral of 1/((x+3)(x+2))	\int\:\frac{1}{(x+3)(x+2)}dx
f(x)=e^xx	f(x)=e^{x}x
integral of (cos(x))/(2-cos(x))	\int\:\frac{\cos(x)}{2-\cos(x)}dx
d/(dy)((x^2)/y)	\frac{d}{dy}(\frac{x^{2}}{y})
integral of ((2-sqrt(x))^7)/(sqrt(x))	\int\:\frac{(2-\sqrt{x})^{7}}{\sqrt{x}}dx
d/(dy)(e^xtan(y))	\frac{d}{dy}(e^{x}\tan(y))

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