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Popular Calculus Problems

(\partial)/(\partial x)(6x^5y^6+8x^7y^8)	\frac{\partial\:}{\partial\:x}(6x^{5}y^{6}+8x^{7}y^{8})
(\partial)/(\partial x)(xarcsin(3x))	\frac{\partial\:}{\partial\:x}(x\arcsin(3x))
f(x)=sin(4x^2)	f(x)=\sin(4x^{2})
limit as x approaches 0 of (cos(2x))/(sin(2x))	\lim\:_{x\to\:0}(\frac{\cos(2x)}{\sin(2x)})
tangent of f(x)=x^3-3x^2+2x-2,\at x=2	tangent\:f(x)=x^{3}-3x^{2}+2x-2,\at\:x=2
derivative of 2/(r^3)	derivative\:\frac{2}{r^{3}}
limit as x approaches 0 of 1/(ln(x))	\lim\:_{x\to\:0}(\frac{1}{\ln(x)})
inverse oflaplace 2/(s(s^2+4))	inverselaplace\:\frac{2}{s(s^{2}+4)}
f(x)=-2cos(2x)	f(x)=-2\cos(2x)
integral from 0 to pi/2 of 9sin^2(3x)	\int\:_{0}^{\frac{π}{2}}9\sin^{2}(3x)dx
sum from n=1 to infinity of ne^{-2n}	\sum\:_{n=1}^{\infty\:}ne^{-2n}
(x+y)dx-(x+y+3)dy=0	(x+y)dx-(x+y+3)dy=0
integral of 6x^2\sqrt[3]{x}	\int\:6x^{2}\sqrt[3]{x}dx
tangent of y=x^3-3x+2,(4,54)	tangent\:y=x^{3}-3x+2,(4,54)
inverse oflaplace (s^2+12)/(s^4-16)	inverselaplace\:\frac{s^{2}+12}{s^{4}-16}
derivative of (x^2/(2-x))	\frac{d}{dx}(\frac{x^{2}}{2-x})
limit as x approaches 0 of sin(x)ln(x)	\lim\:_{x\to\:0}(\sin(x)\ln(x))
integral of (29x^2)/(sqrt(x^2-4))	\int\:\frac{29x^{2}}{\sqrt{x^{2}-4}}dx
area y=x^2+2x,y=x+2	area\:y=x^{2}+2x,y=x+2
integral of 1/8 t	\int\:\frac{1}{8}tdt
derivative of y=sqrt(tan(2x))	derivative\:y=\sqrt{\tan(2x)}
integral of ((x))/((4x^{(2))-12x+25)}	\int\:\frac{(x)}{(4x^{(2)}-12x+25)}dx
limit as x approaches 0+of 1/(1-cos(x))	\lim\:_{x\to\:0+}(\frac{1}{1-\cos(x)})
limit as x approaches 4 of (x-5)/((x-4)^2)	\lim\:_{x\to\:4}(\frac{x-5}{(x-4)^{2}})
xy^'+2y=-4sin(x)	xy^{\prime\:}+2y=-4\sin(x)
tangent of 2x^2+xy+2y^2=5,(1,1)	tangent\:2x^{2}+xy+2y^{2}=5,(1,1)
integral of x(x^2+4)^2	\int\:x(x^{2}+4)^{2}dx
integral of (sec^4(t))/(tan^2(t))	\int\:\frac{\sec^{4}(t)}{\tan^{2}(t)}dt
integral of (tan(ln(5x+6)))/(5x+6)	\int\:\frac{\tan(\ln(5x+6))}{5x+6}dx
derivative of (x^2+2x/(4-5x))	\frac{d}{dx}(\frac{x^{2}+2x}{4-5x})
derivative of y/(sqrt(x^2+y^2))	\frac{d}{dx}(\frac{y}{\sqrt{x^{2}+y^{2}}})
sum from n=0 to infinity of e^2	\sum\:_{n=0}^{\infty\:}e^{2}
derivative of d-ax-b-d/(x^2)	\frac{d}{dx}(d-ax-b-\frac{d}{x^{2}})
tangent of f(x)=tan(x),\at x= pi/4	tangent\:f(x)=\tan(x),\at\:x=\frac{π}{4}
derivative of f(x)=(2-3x-x^2)/(x^2-5)	derivative\:f(x)=\frac{2-3x-x^{2}}{x^{2}-5}
integral of x^e+2/x+sec^2(2x)	\int\:x^{e}+\frac{2}{x}+\sec^{2}(2x)dx
limit as x approaches 0 of (cos(7x)tan(7x))/x	\lim\:_{x\to\:0}(\frac{\cos(7x)\tan(7x)}{x})
tangent of f(x)=(1+x)cos(x),\at x=0	tangent\:f(x)=(1+x)\cos(x),\at\:x=0
tangent of y= 1/3 x^2-2x+4,(3,1)	tangent\:y=\frac{1}{3}x^{2}-2x+4,(3,1)
derivative of cos(tan(4x))	\frac{d}{dx}(\cos(\tan(4x)))
derivative of (x^3-6x^2+5/x)	\frac{d}{dx}(\frac{x^{3}-6x^{2}+5}{x})
sum from n=0 to infinity of (1/6)^n	\sum\:_{n=0}^{\infty\:}(\frac{1}{6})^{n}
(\partial)/(\partial y)(e^{xy})	\frac{\partial\:}{\partial\:y}(e^{xy})
(\partial)/(\partial y)(3cos(y))	\frac{\partial\:}{\partial\:y}(3\cos(y))
limit as x approaches 3 of ((x^4-81))/(x-3)	\lim\:_{x\to\:3}(\frac{(x^{4}-81)}{x-3})
derivative of f(x)=(x^5-4x^3-7)^8	derivative\:f(x)=(x^{5}-4x^{3}-7)^{8}
integral of (32)/(1+16x^2)	\int\:\frac{32}{1+16x^{2}}dx
sum from n=1 to infinity of (1/5)^{n-1}	\sum\:_{n=1}^{\infty\:}(\frac{1}{5})^{n-1}
laplacetransform t+4	laplacetransform\:t+4
laplacetransform 10e^{-10t}	laplacetransform\:10e^{-10t}
derivative of f(x)=ln(x^4)	derivative\:f(x)=\ln(x^{4})
integral of cos(1/3 x)	\int\:\cos(\frac{1}{3}x)dx
inverse oflaplace 1/((s-7)^3)	inverselaplace\:\frac{1}{(s-7)^{3}}
sum from n=1 to infinity of (2n)/(n^2+1)	\sum\:_{n=1}^{\infty\:}\frac{2n}{n^{2}+1}
area y=e^{-3x},x>= 0	area\:y=e^{-3x},x\ge\:0
derivative of 3/(4x^5)	derivative\:\frac{3}{4x^{5}}
limit as x approaches infinity of 1^{2x}	\lim\:_{x\to\:\infty\:}(1^{2x})
limit as x approaches 0+of 7/(1+e^{1/x)}	\lim\:_{x\to\:0+}(\frac{7}{1+e^{\frac{1}{x}}})
sum from n=1 to infinity of n(n+1)x^n	\sum\:_{n=1}^{\infty\:}n(n+1)x^{n}
integral of x^3*2^{-x}	\int\:x^{3}\cdot\:2^{-x}dx
y^{''}+y=0,y(pi/3)=8,y^'(pi/3)=-16	y^{\prime\:\prime\:}+y=0,y(\frac{π}{3})=8,y^{\prime\:}(\frac{π}{3})=-16
inverse oflaplace (s+10)/(s^3(s+2.5)^2)	inverselaplace\:\frac{s+10}{s^{3}(s+2.5)^{2}}
integral of (3x+4)/(sqrt(3x+5))	\int\:\frac{3x+4}{\sqrt{3x+5}}dx
integral from a to p of b/(x(1-x))	\int\:_{a}^{p}\frac{b}{x(1-x)}dx
derivative of \sqrt[6]{x^5}	\frac{d}{dx}(\sqrt[6]{x^{5}})
integral of 1/(2\sqrt[3]{x)+sqrt(x)}	\int\:\frac{1}{2\sqrt[3]{x}+\sqrt{x}}dx
sum from n=0 to infinity of (e^n)/n	\sum\:_{n=0}^{\infty\:}\frac{e^{n}}{n}
(dy)/(dx)=0.5y+x	\frac{dy}{dx}=0.5y+x
derivative of \sqrt[3]{27x^2}-1/(\sqrt[3]{27x^2})	\frac{d}{dx}(\sqrt[3]{27x^{2}}-\frac{1}{\sqrt[3]{27x^{2}}})
integral of (8x^3)/(x^4+5)	\int\:\frac{8x^{3}}{x^{4}+5}dx
limit as x approaches 0-of-1	\lim\:_{x\to\:0-}(-1)
f(x)=8ln(x)-x^2	f(x)=8\ln(x)-x^{2}
derivative of x+3e^{-x}	\frac{d}{dx}(x+3e^{-x})
(\partial)/(\partial y)(5x^{y/z})	\frac{\partial\:}{\partial\:y}(5x^{\frac{y}{z}})
integral of (x^3+3x+4)/(x^4+16x^2)	\int\:\frac{x^{3}+3x+4}{x^{4}+16x^{2}}dx
derivative of (x^2+1/(x-3))	\frac{d}{dx}(\frac{x^{2}+1}{x-3})
limit as x approaches-8 of-3/7 x+10/11	\lim\:_{x\to\:-8}(-\frac{3}{7}x+\frac{10}{11})
derivative of 7/(x-1)	\frac{d}{dx}(\frac{7}{x-1})
limit as x approaches 6-of \sqrt[3]{x-6}	\lim\:_{x\to\:6-}(\sqrt[3]{x-6})
tangent of f(x)=x^2,(2,4)	tangent\:f(x)=x^{2},(2,4)
integral of x+1/x	\int\:x+\frac{1}{x}dx
derivative of ((7x^2-8^4)/x)	\frac{d}{dx}(\frac{(7x^{2}-8)^{4}}{x})
(\partial)/(\partial z)(1)	\frac{\partial\:}{\partial\:z}(1)
taylor e^xcos(x)	taylor\:e^{x}\cos(x)
integral of 6e^2	\int\:6e^{2}dx
(\partial)/(\partial x)(xsin(y-z))	\frac{\partial\:}{\partial\:x}(x\sin(y-z))
integral of (3x-1/x)^2	\int\:(3x-\frac{1}{x})^{2}dx
d/(dy)((y^6)/6+1/(16y^4))	\frac{d}{dy}(\frac{y^{6}}{6}+\frac{1}{16y^{4}})
derivative of 3+t^5+sin(pit)	derivative\:3+t^{5}+\sin(πt)
(dy)/(dx)= y/x-cos(y/x)	\frac{dy}{dx}=\frac{y}{x}-\cos(\frac{y}{x})
integral of (x^4-6x)	\int\:(x^{4}-6x)dx
integral of (sin(20x))/(1+cos^2(20x))	\int\:\frac{\sin(20x)}{1+\cos^{2}(20x)}dx
integral from-8 to 27 of 1/(\sqrt[3]{x)}	\int\:_{-8}^{27}\frac{1}{\sqrt[3]{x}}dx
2y^{''}+35y=0,y(0)=9,y^'(0)=6	2y^{\prime\:\prime\:}+35y=0,y(0)=9,y^{\prime\:}(0)=6
(\partial)/(\partial x)(xe^{x^2-y^2})	\frac{\partial\:}{\partial\:x}(xe^{x^{2}-y^{2}})
y^{''}+y=5e^{-7t}	y^{\prime\:\prime\:}+y=5e^{-7t}
laplacetransform e^{-5t}sin(2t)	laplacetransform\:e^{-5t}\sin(2t)
integral of-x^2+4x	\int\:-x^{2}+4xdx
(2xy-sec^2(x))dx+(x^2+2y)dy=0	(2xy-\sec^{2}(x))dx+(x^{2}+2y)dy=0
integral of ((sqrt(x)+9)/(2\sqrt[3]{x)})	\int\:(\frac{\sqrt{x}+9}{2\sqrt[3]{x}})dx

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