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Popular Calculus Problems

derivative of sqrt(1+x)	derivative\:\sqrt{1+x}
(\partial)/(\partial z)(ze^{xyz})	\frac{\partial\:}{\partial\:z}(ze^{xyz})
(\partial)/(\partial y)(y/(x-y))	\frac{\partial\:}{\partial\:y}(\frac{y}{x-y})
(\partial)/(\partial y)((x+y)^3-12xy)	\frac{\partial\:}{\partial\:y}((x+y)^{3}-12xy)
integral of x*sin(2x^2)	\int\:x\cdot\:\sin(2x^{2})dx
limit as x approaches 0+of x^2e^{1/x}	\lim\:_{x\to\:0+}(x^{2}e^{\frac{1}{x}})
(dy)/(dx)=((1-y^2)/(1-x^2))^{1/2}	\frac{dy}{dx}=(\frac{1-y^{2}}{1-x^{2}})^{\frac{1}{2}}
derivative of 2e^{-2x}+1/3 e^x	\frac{d}{dx}(2e^{-2x}+\frac{1}{3}e^{x})
derivative of 6^{x^2-3}	\frac{d}{dx}(6^{x^{2}-3})
integral from 0 to pi/2 of sin^3(x/2)	\int\:_{0}^{\frac{π}{2}}\sin^{3}(\frac{x}{2})dx
derivative of (x-sqrt(x)/(x^2))	\frac{d}{dx}(\frac{x-\sqrt{x}}{x^{2}})
integral of (x^2)/(x^2-6x+9)	\int\:\frac{x^{2}}{x^{2}-6x+9}dx
tangent of y=(\|x\|)/(sqrt(5-x^2)),(2,2)	tangent\:y=\frac{\left\|x\right\|}{\sqrt{5-x^{2}}},(2,2)
derivative of (2x^2-7)/(8x^3+1)	derivative\:\frac{2x^{2}-7}{8x^{3}+1}
derivative of (sqrt(x^2+y^2-9)/x)	\frac{d}{dx}(\frac{\sqrt{x^{2}+y^{2}-9}}{x})
sum from n=1 to infinity}(-1^{n+1 of)/n	\sum\:_{n=1}^{\infty\:}\frac{-1^{n+1}}{n}
integral of x^2cos(1/2 x)	\int\:x^{2}\cos(\frac{1}{2}x)dx
integral from 0 to 1 of 6/(1+t^2)	\int\:_{0}^{1}\frac{6}{1+t^{2}}dt
derivative of (cos(x)/x+x/(cos(x)))	\frac{d}{dx}(\frac{\cos(x)}{x}+\frac{x}{\cos(x)})
derivative of 1/(sqrt(4x^2+1))	derivative\:\frac{1}{\sqrt{4x^{2}+1}}
limit as x approaches 3-of e^{3/(3-x)}	\lim\:_{x\to\:3-}(e^{\frac{3}{3-x}})
limit as x approaches 0+of (x^2)/9-2/x	\lim\:_{x\to\:0+}(\frac{x^{2}}{9}-\frac{2}{x})
integral of 7^x	\int\:7^{x}dx
integral of 1/(x^{1/2)+x^{3/2}}	\int\:\frac{1}{x^{\frac{1}{2}}+x^{\frac{3}{2}}}dx
(\partial)/(\partial x)(5y^2)	\frac{\partial\:}{\partial\:x}(5y^{2})
tangent of f(x)=sqrt(5x^2-29),\at x=3	tangent\:f(x)=\sqrt{5x^{2}-29},\at\:x=3
integral from-infinity to 0 of 13xe^{3x}	\int\:_{-\infty\:}^{0}13xe^{3x}dx
tangent of f(x)=-5-2x^2,(-3,-23)	tangent\:f(x)=-5-2x^{2},(-3,-23)
y^'+e^xy=2e^x	y^{\prime\:}+e^{x}y=2e^{x}
(dy)/(dx)+y=xye^{-4x}	\frac{dy}{dx}+y=xye^{-4x}
integral of sin(θ)e^{cos(θ)}	\int\:\sin(θ)e^{\cos(θ)}dθ
integral from 1 to 3 of sqrt(x)	\int\:_{1}^{3}\sqrt{x}dx
integral of e^{2x}cos(4x)	\int\:e^{2x}\cos(4x)dx
derivative of (ln(x)^{-2})	\frac{d}{dx}((\ln(x))^{-2})
integral of 2x^{1/3}	\int\:2x^{\frac{1}{3}}dx
limit as x approaches infinity of cos(x)	\lim\:_{x\to\:\infty\:}(\cos(x))
y^{''}+12y^'+36y=e^{-5x}(x^2-2x+3)	y^{\prime\:\prime\:}+12y^{\prime\:}+36y=e^{-5x}(x^{2}-2x+3)
derivative of (e^{x-2})/(x-1)	derivative\:\frac{e^{x-2}}{x-1}
sum from n=0 to infinity of 1/((2n)!)	\sum\:_{n=0}^{\infty\:}\frac{1}{(2n)!}
area y=\sqrt[3]{2x},y= 1/8 x^2	area\:y=\sqrt[3]{2x},y=\frac{1}{8}x^{2}
derivative of arctan(sqrt(x^2+2x)+C)	\frac{d}{dx}(\arctan(\sqrt{x^{2}+2x})+C)
integral of x/(sqrt(1+5x^2))	\int\:\frac{x}{\sqrt{1+5x^{2}}}dx
derivative of y=3x^2+1/x	derivative\:y=3x^{2}+\frac{1}{x}
integral of x^e	\int\:x^{e}dx
integral of 2/(e^xsqrt(11+e^{2x))}	\int\:\frac{2}{e^{x}\sqrt{11+e^{2x}}}dx
integral of 7cos^3(3x)	\int\:7\cos^{3}(3x)dx
xy^'+3y=0	xy^{\prime\:}+3y=0
limit as x approaches 0+of 3	\lim\:_{x\to\:0+}(3)
derivative of f(x)=cos(2sin(x))	derivative\:f(x)=\cos(2\sin(x))
derivative of y=ln(e^x+xe^x)	derivative\:y=\ln(e^{x}+xe^{x})
derivative of 3(9x-4^4)	\frac{d}{dx}(3(9x-4)^{4})
integral of x/((x-1)^3)	\int\:\frac{x}{(x-1)^{3}}dx
y^'+2*y=t	y^{\prime\:}+2\cdot\:y=t
derivative of ln(x+sqrt(4+x^2))	\frac{d}{dx}(\ln(x+\sqrt{4+x^{2}}))
(\partial)/(\partial x)(e^xln(xy))	\frac{\partial\:}{\partial\:x}(e^{x}\ln(xy))
derivative of 2x^3-3x^2-12+8	derivative\:2x^{3}-3x^{2}-12+8
sum from n=1 to infinity of 7^nx^{n-1}	\sum\:_{n=1}^{\infty\:}7^{n}x^{n-1}
y^{''}+6y^'+8y=cos(3t),y(0)=-2,y^'(0)=1	y^{\prime\:\prime\:}+6y^{\prime\:}+8y=\cos(3t),y(0)=-2,y^{\prime\:}(0)=1
integral from 6 to 8 of (86)/((x-6)^3)	\int\:_{6}^{8}\frac{86}{(x-6)^{3}}dx
(\partial)/(\partial x)(2x^4y^2+3x^2y^4)	\frac{\partial\:}{\partial\:x}(2x^{4}y^{2}+3x^{2}y^{4})
integral of (cos(e^{-x}))/(e^{2x)}	\int\:\frac{\cos(e^{-x})}{e^{2x}}dx
sum from k=1 to infinity of (4k)/(7k-1)	\sum\:_{k=1}^{\infty\:}\frac{4k}{7k-1}
laplacetransform 5cos(2t)	laplacetransform\:5\cos(2t)
integral from 1 to 0 of x^2	\int\:_{1}^{0}x^{2}dx
derivative of sin^3(2x+x^2)	\frac{d}{dx}(\sin^{3}(2x)+x^{2})
y^{''}-4y+3y=0	y^{\prime\:\prime\:}-4y+3y=0
integral of (5x^2+2x)/(x^2-5x-6)	\int\:\frac{5x^{2}+2x}{x^{2}-5x-6}dx
(dy}{dx}=\frac{y(ln(y)-ln(x)+1))/x	\frac{dy}{dx}=\frac{y(\ln(y)-\ln(x)+1)}{x}
area 2x,x^2-3	area\:2x,x^{2}-3
integral from-2 to 3 of 2xsqrt(2x^2-3)	\int\:_{-2}^{3}2x\sqrt{2x^{2}-3}dx
(\partial}{\partial t}(\frac{r+s)/t)	\frac{\partial\:}{\partial\:t}(\frac{r+s}{t})
integral of (sqrt(5x)+sqrt(5/x))	\int\:(\sqrt{5x}+\sqrt{\frac{5}{x}})dx
(\partial)/(\partial x)(x^2-xy+2y^2)	\frac{\partial\:}{\partial\:x}(x^{2}-xy+2y^{2})
implicit y^2=x^2-xc	implicit\:y^{2}=x^{2}-xc
derivative of (5x/(1+x^2))	\frac{d}{dx}(\frac{5x}{1+x^{2}})
limit as x approaches 1 of x/(4x-1)	\lim\:_{x\to\:1}(\frac{x}{4x-1})
tangent of f(x)=x^2,(-4,15)	tangent\:f(x)=x^{2},(-4,15)
derivative of (8x^2-16x+16)e^x	derivative\:(8x^{2}-16x+16)e^{x}
limit as x approaches 1 of ln(e^x-1)	\lim\:_{x\to\:1}(\ln(e^{x}-1))
derivative of ((x+2)/((x+1)))	\frac{d}{dx}(\frac{(x+2)}{(x+1)})
integral of (1-e^{-x})	\int\:(1-e^{-x})dx
(d^2y)/(dx^2)-3(dy)/(dx)+2y=10sin(x)	\frac{d^{2}y}{dx^{2}}-3\frac{dy}{dx}+2y=10\sin(x)
integral of 2sin(sqrt(x))	\int\:2\sin(\sqrt{x})dx
limit as x approaches 1 of-2x^2+5x+4	\lim\:_{x\to\:1}(-2x^{2}+5x+4)
derivative of (x^2/(x^2+y^2))	\frac{d}{dx}(\frac{x^{2}}{x^{2}+y^{2}})
derivative of sin^{1/2}(x)	\frac{d}{dx}(\sin^{\frac{1}{2}}(x))
derivative of 10x+9x^2+3y	\frac{d}{dx}(10x+9x^{2}+3y)
implicit (dy)/(dx),y=arcsin(2x+1)	implicit\:\frac{dy}{dx},y=\arcsin(2x+1)
taylor e^{(t^2)/2}	taylor\:e^{\frac{t^{2}}{2}}
(\partial)/(\partial x)(((xy^2))/(x^2+y^2))	\frac{\partial\:}{\partial\:x}(\frac{(xy^{2})}{x^{2}+y^{2}})
integral of (csc^2(2x))/(4-cot(2x))	\int\:\frac{\csc^{2}(2x)}{4-\cot(2x)}dx
integral from-1 to 1 of x(1-x^2)	\int\:_{-1}^{1}x(1-x^{2})dx
integral of sin^2(x)cos(nx)	\int\:\sin^{2}(x)\cos(nx)dx
derivative of (cos(sqrt(x))/(2sqrt(x)))	\frac{d}{dx}(\frac{\cos(\sqrt{x})}{2\sqrt{x}})
tangent of f(x)=9-3x+2x^2,\at x=-6	tangent\:f(x)=9-3x+2x^{2},\at\:x=-6
derivative of 2x-3x^{2/3}	\frac{d}{dx}(2x-3x^{\frac{2}{3}})
integral of 25e^{-2x}	\int\:25e^{-2x}dx
limit as x approaches 3-of x-2	\lim\:_{x\to\:3-}(x-2)
limit as x approaches pi/2-of cot(2x)	\lim\:_{x\to\:\frac{π}{2}-}(\cot(2x))
(dy)/(dx)=x^3y	\frac{dy}{dx}=x^{3}y

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