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Popular Calculus Problems

derivative of 8^{x^3}	\frac{d}{dx}(8^{x^{3}})
(dy)/(dt)=4y+y^3	\frac{dy}{dt}=4y+y^{3}
integral of e^{nx}sin(nx)	\int\:e^{nx}\sin(nx)dx
limit as x approaches 0 of xsin(6/x)	\lim\:_{x\to\:0}(x\sin(\frac{6}{x}))
derivative of x/(ln(2x))	\frac{d}{dx}(\frac{x}{\ln(2x)})
integral of 30t^5e^{-t^6}	\int\:30t^{5}e^{-t^{6}}dt
derivative of (sqrt(x)/(9+x))	\frac{d}{dx}(\frac{\sqrt{x}}{9+x})
integral of (x^2+3x+1)/((x^2+1)^2)	\int\:\frac{x^{2}+3x+1}{(x^{2}+1)^{2}}dx
integral of ((e^{2x}))/(4+e^{4x)}	\int\:\frac{(e^{2x})}{4+e^{4x}}dx
integral of l	\int\:ldl
limit as x approaches 1 of 9/(x^3-1)	\lim\:_{x\to\:1}(\frac{9}{x^{3}-1})
derivative of y=7arctan(x-sqrt(1+x^2))	derivative\:y=7\arctan(x-\sqrt{1+x^{2}})
integral from 0 to 3 of 2pix(3x-x^2)	\int\:_{0}^{3}2πx(3x-x^{2})dx
(\partial)/(\partial x)(cos(5x+9y+4z))	\frac{\partial\:}{\partial\:x}(\cos(5x+9y+4z))
y^'=y-y^2,y(0)=10	y^{\prime\:}=y-y^{2},y(0)=10
derivative of 2x^{9/2}	\frac{d}{dx}(2x^{\frac{9}{2}})
derivative of sin(xx^{-2})	\frac{d}{dx}(\sin(x)x^{-2})
integral of e^{-nx}	\int\:e^{-nx}dx
(x(dy)/(dx)+2y)=3	(x\frac{dy}{dx}+2y)=3
tangent of f(x)=sqrt(9-x),\at x=2	tangent\:f(x)=\sqrt{9-x},\at\:x=2
y^'=e^{8x+y}	y^{\prime\:}=e^{8x+y}
(\partial)/(\partial y)(ze^{xy})	\frac{\partial\:}{\partial\:y}(ze^{xy})
limit as x approaches 1 of 3x^3-4x^2+x+2	\lim\:_{x\to\:1}(3x^{3}-4x^{2}+x+2)
(\partial)/(\partial x)(ln(x^3+y)-z)	\frac{\partial\:}{\partial\:x}(\ln(x^{3}+y)-z)
integral of (x^{10})/((x^2+x-2))	\int\:\frac{x^{10}}{(x^{2}+x-2)}dx
derivative of e^{-1/2}	\frac{d}{dx}(e^{-\frac{1}{2}})
derivative of f(x)= 1/2 x^2-2x+6	derivative\:f(x)=\frac{1}{2}x^{2}-2x+6
x*(dy)/(dx)=2y	x\cdot\:\frac{dy}{dx}=2y
integral of (csc(x)-tan(x))^2	\int\:(\csc(x)-\tan(x))^{2}dx
integral from 2 to 6 of t^2ln(2t)	\int\:_{2}^{6}t^{2}\ln(2t)dt
tangent of y=(7x)/(x-3),(6,14)	tangent\:y=\frac{7x}{x-3},(6,14)
derivative of-6\sqrt[3]{x^2}	derivative\:-6\sqrt[3]{x^{2}}
derivative of (x)^2	derivative\:(x)^{2}
(\partial)/(\partial y)(y+x)	\frac{\partial\:}{\partial\:y}(y+x)
area y= 1/((9x^3)),1,100	area\:y=\frac{1}{(9x^{3})},1,100
20y^{''}+4y^'+y=0	20y^{\prime\:\prime\:}+4y^{\prime\:}+y=0
(x+sqrt(x))^'	(x+\sqrt{x})^{\prime\:}
integral of 8/((x-2)^2)	\int\:\frac{8}{(x-2)^{2}}dx
7x(x+y)y^'=7y(x-y)	7x(x+y)y^{\prime\:}=7y(x-y)
(\partial)/(\partial x)(8x^{0.5}y^{0.5})	\frac{\partial\:}{\partial\:x}(8x^{0.5}y^{0.5})
derivative of-(2(-3x^2+1)/((x^2+1)^3))	\frac{d}{dx}(-\frac{2(-3x^{2}+1)}{(x^{2}+1)^{3}})
tangent of f(x)=x^3-4x+6,(2,6)	tangent\:f(x)=x^{3}-4x+6,(2,6)
derivative of f(x)=x^2(2+x^{-3})	derivative\:f(x)=x^{2}(2+x^{-3})
(\partial)/(\partial x)(xy^2-2x)	\frac{\partial\:}{\partial\:x}(xy^{2}-2x)
integral of (14)/(x^2+1)	\int\:\frac{14}{x^{2}+1}dx
derivative of e^{{f}(x})	\frac{d}{dx}(e^{{f}(x)})
tangent of y=10xsin(x),(pi/2 ,5pi)	tangent\:y=10x\sin(x),(\frac{π}{2},5π)
y^'-5y=x	y^{\prime\:}-5y=x
integral of sec^4(xta)n^3x	\int\:\sec^{4}(xta)n^{3}xdx
integral of sin(θ)cos(θ)	\int\:\sin(θ)\cos(θ)dθ
integral of+sin^2(4x)cos^2(4x)	\int\:+\sin^{2}(4x)\cos^{2}(4x)dx
taylor 8x^4-1x^2+9x+2,x=0.05	taylor\:8x^{4}-1x^{2}+9x+2,x=0.05
limit as x approaches 1 of (x^2-1)/(sqrt(2x+1)-\sqrt{3)}	\lim\:_{x\to\:1}(\frac{x^{2}-1}{\sqrt{2x+1}-\sqrt{3}})
derivative of 2log_{5}(t)	derivative\:2\log_{5}(t)
(y-x5)dx+(x+y5)dy=0	(y-x5)dx+(x+y5)dy=0
integral of sin^2(θ)cos(θ)	\int\:\sin^{2}(θ)\cos(θ)dθ
integral of ((3x-2)^2+(3x+2)^2)/(x^2)	\int\:\frac{(3x-2)^{2}+(3x+2)^{2}}{x^{2}}dx
derivative of (cos(2x))/(sqrt(sin(2x)))	derivative\:\frac{\cos(2x)}{\sqrt{\sin(2x)}}
integral of (4x^5+3x+8)	\int\:(4x^{5}+3x+8)dx
f^'(x)=8x^3-6x^2+10x-9,f(1)=24	f^{\prime\:}(x)=8x^{3}-6x^{2}+10x-9,f(1)=24
maclaurin sqrt(1-x^2)	maclaurin\:\sqrt{1-x^{2}}
derivative of y=(sqrt(x))/(7+x)	derivative\:y=\frac{\sqrt{x}}{7+x}
limit as x approaches 1 of sqrt(7x+42)	\lim\:_{x\to\:1}(\sqrt{7x+42})
derivative of 5^{mx}	\frac{d}{dx}(5^{mx})
integral of sqrt(4-\sqrt{x)}	\int\:\sqrt{4-\sqrt{x}}dx
limit as x approaches-10 of 1/(x+10)	\lim\:_{x\to\:-10}(\frac{1}{x+10})
limit as x approaches 0-of e^x	\lim\:_{x\to\:0-}(e^{x})
integral from 0 to 2pi of cos(t)sin(t)	\int\:_{0}^{2π}\cos(t)\sin(t)dt
integral of x*\sqrt[3]{x-2}	\int\:x\cdot\:\sqrt[3]{x-2}dx
integral of 3/2 (x+1)^{1/2}	\int\:\frac{3}{2}(x+1)^{\frac{1}{2}}dx
limit as x approaches-1/2 of ((6x-1))/x	\lim\:_{x\to\:-\frac{1}{2}}(\frac{(6x-1)}{x})
derivative of 17^x	derivative\:17^{x}
derivative of pi-x	\frac{d}{dx}(π-x)
derivative of (sqrt(x))/(x+2)	derivative\:\frac{\sqrt{x}}{x+2}
y^'=y^2+xy^2	y^{\prime\:}=y^{2}+xy^{2}
integral of 7/(x(x^4+6))	\int\:\frac{7}{x(x^{4}+6)}dx
sum from k=1 to infinity of 1/(2^k)	\sum\:_{k=1}^{\infty\:}\frac{1}{2^{k}}
3x+y-2+(dy)/(dx)(x-1)=0	3x+y-2+\frac{dy}{dx}(x-1)=0
sum from n=0 to infinity of 1/(2n+1)	\sum\:_{n=0}^{\infty\:}\frac{1}{2n+1}
integral of 1/(1+4x^2+4x^4)	\int\:\frac{1}{1+4x^{2}+4x^{4}}dx
limit as x approaches pi/4 of 2sin(3x)	\lim\:_{x\to\:\frac{π}{4}}(2\sin(3x))
derivative of (1-x^4^3)	\frac{d}{dx}((1-x^{4})^{3})
integral of sqrt(6x+4)	\int\:\sqrt{6x+4}dx
(\partial)/(\partial x)(3y-(x^2+1))	\frac{\partial\:}{\partial\:x}(3y-(x^{2}+1))
integral of \sqrt[5]{x}	\int\:\sqrt[5]{x}dx
(\partial)/(\partial y)(1-3/y+x)	\frac{\partial\:}{\partial\:y}(1-\frac{3}{y}+x)
derivative of f(x)=(x+1)^{x+1}	derivative\:f(x)=(x+1)^{x+1}
derivative of y=sin(9x)+cos(7x)	derivative\:y=\sin(9x)+\cos(7x)
derivative of sqrt(2-5x^2)	\frac{d}{dx}(\sqrt{2-5x^{2}})
integral from 2 to 3 of 1/(3x-2)	\int\:_{2}^{3}\frac{1}{3x-2}dx
f(x)=x^e	f(x)=x^{e}
limit as x approaches 0 of (tan(6x))/x	\lim\:_{x\to\:0}(\frac{\tan(6x)}{x})
derivative of f(x)=3e^xsqrt(x)	derivative\:f(x)=3e^{x}\sqrt{x}
(\partial)/(\partial x)((2s-3y)/(3s+5y))	\frac{\partial\:}{\partial\:x}(\frac{2s-3y}{3s+5y})
integral of ((x+3))/(x^2)	\int\:\frac{(x+3)}{x^{2}}dx
limit as x approaches pi/3 of tan(x)	\lim\:_{x\to\:\frac{π}{3}}(\tan(x))
derivative of axe^x+ae^x	\frac{d}{dx}(axe^{x}+ae^{x})
derivative of-3x^4+4x^3+2	\frac{d}{dx}(-3x^{4}+4x^{3}+2)
integral of 3e^{-st}	\int\:3e^{-st}dt
integral of-3cos(5x)	\int\:-3\cos(5x)dx

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