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Popular Calculus Problems

(\partial)/(\partial x)(3xy-x^2y-xy^2)	\frac{\partial\:}{\partial\:x}(3xy-x^{2}y-xy^{2})
y^'=(4y+21)^{(1/2)}	y^{\prime\:}=(4y+21)^{(\frac{1}{2})}
(dy)/(dx)=-y	\frac{dy}{dx}=-y
(\partial)/(\partial x)(2y-2cos(x))	\frac{\partial\:}{\partial\:x}(2y-2\cos(x))
6t^2y^{''}-12y=14t^2-1	6t^{2}y^{\prime\:\prime\:}-12y=14t^{2}-1
integral of x/((x+1)(x+2)(x+3))	\int\:\frac{x}{(x+1)(x+2)(x+3)}dx
derivative of (e^x/(3x))	\frac{d}{dx}(\frac{e^{x}}{3x})
(\partial)/(\partial x)(ln(x+y)+xcos(y))	\frac{\partial\:}{\partial\:x}(\ln(x+y)+x\cos(y))
integral from 0 to 3 of (7t)/((t-4)^2)	\int\:_{0}^{3}\frac{7t}{(t-4)^{2}}dt
derivative of 7x^e+e^{9x}	derivative\:7x^{e}+e^{9x}
derivative of f(x)=(x^2)/(5+sqrt(x))	derivative\:f(x)=\frac{x^{2}}{5+\sqrt{x}}
integral of (a^2-x^2)^{5/2}	\int\:(a^{2}-x^{2})^{\frac{5}{2}}dx
integral of 4x^3-10x	\int\:4x^{3}-10xdx
integral of (4t^3-t^2+16t)/(t^2+4)	\int\:\frac{4t^{3}-t^{2}+16t}{t^{2}+4}dt
sum from n=1 to infinity of n/(n^2+3)	\sum\:_{n=1}^{\infty\:}\frac{n}{n^{2}+3}
integral of (xy^2-cos(x)sin(x))	\int\:(xy^{2}-\cos(x)\sin(x))dx
y^'-2xy=8x	y^{\prime\:}-2xy=8x
integral of (x^4+sec^2(x))	\int\:(x^{4}+\sec^{2}(x))dx
derivative of xe^{yx}	\frac{d}{dx}(xe^{yx})
derivative of e^{-x}cos(3x)	\frac{d}{dx}(e^{-x}\cos(3x))
integral from 1 to 3 of sqrt(t)ln(t)	\int\:_{1}^{3}\sqrt{t}\ln(t)dt
integral of \sqrt[3]{x^{11}}	\int\:\sqrt[3]{x^{11}}dx
derivative of (1/5)(xy^2+4y)^2	derivative\:(\frac{1}{5})(xy^{2}+4y)^{2}
integral of x*cos(x)	\int\:x\cdot\:\cos(x)dx
derivative of ln(x^3+e^{2x})	\frac{d}{dx}(\ln(x^{3})+e^{2x})
(dy)/(dx)=sqrt(7y)*e^{(x+9)}	\frac{dy}{dx}=\sqrt{7y}\cdot\:e^{(x+9)}
integral of (e^x)/((e^x-3)(e^x+2))	\int\:\frac{e^{x}}{(e^{x}-3)(e^{x}+2)}dx
derivative of f(x)=csc^7(2x^pi+pi^3)	derivative\:f(x)=\csc^{7}(2x^{π}+π^{3})
normal of y=x^2-7x+7,(4,0)	normal\:y=x^{2}-7x+7,(4,0)
y^{''}-9y=0	y^{\prime\:\prime\:}-9y=0
derivative of (2x^2+4x+2/(sqrt(x)))	\frac{d}{dx}(\frac{2x^{2}+4x+2}{\sqrt{x}})
(dy)/(dx)=(-y^2)/(1+y^2)e^{-x}	\frac{dy}{dx}=\frac{-y^{2}}{1+y^{2}}e^{-x}
limit as x approaches 2-of (x^3+1)/(x-2)	\lim\:_{x\to\:2-}(\frac{x^{3}+1}{x-2})
integral of 1/((x+5)^2(x-3))	\int\:\frac{1}{(x+5)^{2}(x-3)}dx
(\partial)/(\partial y)(4xy-x^4-y^4+1)	\frac{\partial\:}{\partial\:y}(4xy-x^{4}-y^{4}+1)
sum from n=2 to infinity of ((3x-2)^n)/n	\sum\:_{n=2}^{\infty\:}\frac{(3x-2)^{n}}{n}
derivative of g(x)=5x^2tan(1-sqrt(x))	derivative\:g(x)=5x^{2}\tan(1-\sqrt{x})
integral of x/(x^2-15)	\int\:\frac{x}{x^{2}-15}dx
derivative of y=sin(2t)	derivative\:y=\sin(2t)
integral of 4cos^4(5x)	\int\:4\cos^{4}(5x)dx
f(x)=(e^x)/(1+e^x)	f(x)=\frac{e^{x}}{1+e^{x}}
derivative of f(x)=(x^2+2x-2)/((x+1)^2)	derivative\:f(x)=\frac{x^{2}+2x-2}{(x+1)^{2}}
d/(dt)(6cos(t))	\frac{d}{dt}(6\cos(t))
integral from 1 to 2 of x^{-2}	\int\:_{1}^{2}x^{-2}dx
area y=(16)/(x^2-6x-55),x=-3,x=3	area\:y=\frac{16}{x^{2}-6x-55},x=-3,x=3
integral of (x^2+132x+132)/(x^3-4x)	\int\:\frac{x^{2}+132x+132}{x^{3}-4x}dx
integral of (e^x)/(e^{2x)-e^x}	\int\:\frac{e^{x}}{e^{2x}-e^{x}}dx
(\partial)/(\partial z)(ln(x))	\frac{\partial\:}{\partial\:z}(\ln(x))
integral of x/(3x^2-1)	\int\:\frac{x}{3x^{2}-1}dx
slope of (-10.9)(-12.7)	slope\:(-10.9)(-12.7)
derivative of sin((2x)/(x+1))	derivative\:\sin(\frac{2x}{x+1})
integral of 7x^2y+3/x-1	\int\:7x^{2}y+\frac{3}{x}-1dx
(\partial)/(\partial x)(12y^2x^2-6yx)	\frac{\partial\:}{\partial\:x}(12y^{2}x^{2}-6yx)
derivative of sin^4(4x)	\frac{d}{dx}(\sin^{4}(4x))
(dx)/(dy)=3x(5-x)	\frac{dx}{dy}=3x(5-x)
(3t+6y+3)=(dy)/(dt)	(3t+6y+3)=\frac{dy}{dt}
derivative of x	derivative\:x
integral of sqrt(1-\sqrt{x)}	\int\:\sqrt{1-\sqrt{x}}dx
tangent of y=-x^3,(-2,8)	tangent\:y=-x^{3},(-2,8)
limit as x approaches+0 of arctan(x)	\lim\:_{x\to\:+0}(\arctan(x))
derivative of 7/(\sqrt[3]{x})	\frac{d}{dx}(\frac{7}{\sqrt[3]{x}})
(dy)/(dx)=(y-1)^2	\frac{dy}{dx}=(y-1)^{2}
taylor 1/((1-x))	taylor\:\frac{1}{(1-x)}
limit as x approaches 0 of \sqrt[4]{x}	\lim\:_{x\to\:0}(\sqrt[4]{x})
integral of sin(x)cos^4(x	\int\:\sin(x)\cos^{4}(d)xdx
y^'=((e^{x-y}))/((1+e^x))	y^{\prime\:}=\frac{(e^{x-y})}{(1+e^{x})}
derivative of csc^2(x-3)	\frac{d}{dx}(\csc^{2}(x)-3)
derivative of log_{9}(x)	\frac{d}{dx}(\log_{9}(x))
sum from n=1 to infinity of (cos(1))^n	\sum\:_{n=1}^{\infty\:}(\cos(1))^{n}
du= 1/(2sqrt(x))dx	du=\frac{1}{2\sqrt{x}}dx
derivative of (7e^ss-6e^s)/((7s+1)^2)	derivative\:\frac{7e^{s}s-6e^{s}}{(7s+1)^{2}}
limit as x approaches 81 of (x^2)/9-9/x	\lim\:_{x\to\:81}(\frac{x^{2}}{9}-\frac{9}{x})
(\partial)/(\partial s)(3st)	\frac{\partial\:}{\partial\:s}(3st)
(\partial)/(\partial x)(ln(sec(x)))	\frac{\partial\:}{\partial\:x}(\ln(\sec(x)))
sum from n=1 to infinity of 1/(2^{2n)}	\sum\:_{n=1}^{\infty\:}\frac{1}{2^{2n}}
integral of (4csc^2(t)-3e^t)	\int\:(4\csc^{2}(t)-3e^{t})dt
integral of e^{3x}cos(5x)	\int\:e^{3x}\cos(5x)dx
integral of (e^{ln(x)})/x	\int\:\frac{e^{\ln(x)}}{x}dx
derivative of sqrt(5x+9)	\frac{d}{dx}(\sqrt{5x+9})
(dy)/(dx)=(x+y+8)^2	\frac{dy}{dx}=(x+y+8)^{2}
y^{''}+2y+y=1	y^{\prime\:\prime\:}+2y+y=1
(\partial)/(\partial x)(x/((x^2+y^2)^2))	\frac{\partial\:}{\partial\:x}(\frac{x}{(x^{2}+y^{2})^{2}})
integral of x^2sqrt(2-x^3)	\int\:x^{2}\sqrt{2-x^{3}}dx
taylor cos(x),\at pi/2	taylor\:\cos(x),\at\:\frac{π}{2}
(\partial)/(\partial y)((x-y)(1-xy))	\frac{\partial\:}{\partial\:y}((x-y)(1-xy))
xy^'+2y=(4e^{3x})/x	xy^{\prime\:}+2y=\frac{4e^{3x}}{x}
derivative of f(x)=2x^3-21x^2+72x-5	derivative\:f(x)=2x^{3}-21x^{2}+72x-5
(\partial)/(\partial x)(e^{2x-y})	\frac{\partial\:}{\partial\:x}(e^{2x-y})
limit as x approaches 0 of (x-14)/(x-2)	\lim\:_{x\to\:0}(\frac{x-14}{x-2})
limit as x approaches 0+of 1/(x^2)	\lim\:_{x\to\:0+}(\frac{1}{x^{2}})
integral of-30t^{2/3}	\int\:-30t^{\frac{2}{3}}dt
inverse oflaplace s/(2(s^2+4s+6))	inverselaplace\:\frac{s}{2(s^{2}+4s+6)}
integral from-2 to 2 of (x^2-1)	\int\:_{-2}^{2}(x^{2}-1)dx
limit as x approaches-5 of x^2-5	\lim\:_{x\to\:-5}(x^{2}-5)
limit as x approaches 4 of (3x^2-8x-16)/(2x^2-9x+4)	\lim\:_{x\to\:4}(\frac{3x^{2}-8x-16}{2x^{2}-9x+4})
(\partial)/(\partial x)(e^{x+y}(x-1)(y-2))	\frac{\partial\:}{\partial\:x}(e^{x+y}(x-1)(y-2))
inverse oflaplace (s+1)/((s+1)^2+4)	inverselaplace\:\frac{s+1}{(s+1)^{2}+4}
integral of x^2sqrt(4x+8)	\int\:x^{2}\sqrt{4x+8}dx
area y=x^2,y=sqrt(4+x)	area\:y=x^{2},y=\sqrt{4+x}
integral of x(x-3)^2+4^2	\int\:x(x-3)^{2}+4^{2}dx

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