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Popular Calculus Problems

tangent of f(x)=(2x)/(1+x^2),\at x=(4)	tangent\:f(x)=\frac{2x}{1+x^{2}},\at\:x=(4)
xy^'-2y=x^4,y(1)=0	xy^{\prime\:}-2y=x^{4},y(1)=0
limit as x approaches 9 of \sqrt[3]{x-9}	\lim\:_{x\to\:9}(\sqrt[3]{x-9})
derivative of (4x-8e^{4x})	\frac{d}{dx}((4x-8)e^{4x})
derivative of x^{5pi}	derivative\:x^{5π}
(\partial)/(\partial x)(sqrt(10x+8y))	\frac{\partial\:}{\partial\:x}(\sqrt{10x+8y})
(\partial)/(\partial y)((xy+3x^2)/(1+y))	\frac{\partial\:}{\partial\:y}(\frac{xy+3x^{2}}{1+y})
integral of cos(2x)e^{sin(2x)}	\int\:\cos(2x)e^{\sin(2x)}dx
derivative of (3x-10/(7x+13))	\frac{d}{dx}(\frac{3x-10}{7x+13})
derivative of f(x)=-4/3 x^{-5/2}	derivative\:f(x)=-\frac{4}{3}x^{-\frac{5}{2}}
integral of (sqrt(9x^2+4))/(x^2)	\int\:\frac{\sqrt{9x^{2}+4}}{x^{2}}dx
integral of 6t^5	\int\:6t^{5}dt
x^2y^'-3xy-2y^2=0	x^{2}y^{\prime\:}-3xy-2y^{2}=0
(dy)/(dt)+2/t y=t-1+y/t	\frac{dy}{dt}+\frac{2}{t}y=t-1+\frac{y}{t}
tangent of y=9x^{5/2}-7x^{3/2},\at x=4	tangent\:y=9x^{\frac{5}{2}}-7x^{\frac{3}{2}},\at\:x=4
(dy)/(dx)-2(x+1)^3= 4/((x+1))y	\frac{dy}{dx}-2(x+1)^{3}=\frac{4}{(x+1)}y
derivative of f(x)=arctan(pi/x)	derivative\:f(x)=\arctan(\frac{π}{x})
y^'=6y^2sin(x)	y^{\prime\:}=6y^{2}\sin(x)
integral of 1/((9x-1)^2)	\int\:\frac{1}{(9x-1)^{2}}dx
integral from-14 to 7 of (7e^x)	\int\:_{-14}^{7}(7e^{x})dx
integral from 0 to 3 of (3x^2-4x+1)	\int\:_{0}^{3}(3x^{2}-4x+1)dx
derivative of xsin(y/x)	\frac{d}{dx}(x\sin(\frac{y}{x}))
(\partial)/(\partial x)(cos(x)cos(y)e^z)	\frac{\partial\:}{\partial\:x}(\cos(x)\cos(y)e^{z})
integral of 1/((x-7)^2)	\int\:\frac{1}{(x-7)^{2}}dx
y^{''}-5y^'-6y=12e^{2t}	y^{\prime\:\prime\:}-5y^{\prime\:}-6y=12e^{2t}
limit as x approaches 0 of 1/((x-1)^2)+2	\lim\:_{x\to\:0}(\frac{1}{(x-1)^{2}}+2)
(dy)/(dx)+10y=11	\frac{dy}{dx}+10y=11
derivative of x^2-4x+10	\frac{d}{dx}(x^{2}-4x+10)
derivative of 6e^x+4/(\sqrt[3]{x})	\frac{d}{dx}(6e^{x}+\frac{4}{\sqrt[3]{x}})
limit as x approaches 5 of 1/(x^2-1)	\lim\:_{x\to\:5}(\frac{1}{x^{2}-1})
derivative of (2x^2+8x+4/(sqrt(x)))	\frac{d}{dx}(\frac{2x^{2}+8x+4}{\sqrt{x}})
y^{''}+31y=0	y^{\prime\:\prime\:}+31y=0
derivative of-8x^{1/2}	\frac{d}{dx}(-8x^{\frac{1}{2}})
tangent of sqrt(5x+6),\at x=6	tangent\:\sqrt{5x+6},\at\:x=6
integral of xe^{-sx}	\int\:xe^{-sx}dx
(\partial)/(\partial x)(8x^5y^3-9x^4y^6)	\frac{\partial\:}{\partial\:x}(8x^{5}y^{3}-9x^{4}y^{6})
derivative of (4x^3+1/(x^2-x+3))	\frac{d}{dx}(\frac{4x^{3}+1}{x^{2}-x+3})
(dy}{dx}-y/x =\frac{sqrt(x^2+y^2))/x	\frac{dy}{dx}-\frac{y}{x}=\frac{\sqrt{x^{2}+y^{2}}}{x}
derivative of f(x)=e^{1/2 x}	derivative\:f(x)=e^{\frac{1}{2}x}
derivative of x+7	\frac{d}{dx}(x+7)
implicit (dy)/(dx),x^2+5x+9xy-y^2=4	implicit\:\frac{dy}{dx},x^{2}+5x+9xy-y^{2}=4
1+6x^{3/2}	1+6x^{\frac{3}{2}}
integral of 1/(3+sqrt(x+2))	\int\:\frac{1}{3+\sqrt{x+2}}dx
y^{''}-2y^'-3y=64xe^{-x}	y^{\prime\:\prime\:}-2y^{\prime\:}-3y=64xe^{-x}
integral from 0 to a of (m/(2pi(a-x)))^5	\int\:_{0}^{a}(\frac{m}{2π(a-x)})^{5}dx
area y=3x^4-3x^2,y=3x^2	area\:y=3x^{4}-3x^{2},y=3x^{2}
limit as x approaches 2 of (2x+4)/(x-7)	\lim\:_{x\to\:2}(\frac{2x+4}{x-7})
integral of 10^{-3x}	\int\:10^{-3x}dx
derivative of (e^x^3)	\frac{d}{dx}((e^{x})^{3})
derivative of (x-1^2sin(1/(x-1)))	\frac{d}{dx}((x-1)^{2}\sin(\frac{1}{x-1}))
derivative of (x^2+2x-6)/((x+1)^2)	derivative\:\frac{x^{2}+2x-6}{(x+1)^{2}}
derivative of 4/(sqrt(x))	derivative\:\frac{4}{\sqrt{x}}
derivative of 3+1/4 sin(3pit)	derivative\:3+\frac{1}{4}\sin(3πt)
integral of x^2sqrt(x^3+21)	\int\:x^{2}\sqrt{x^{3}+21}dx
integral of+(x^2)/((225+x^2)^2)	\int\:+\frac{x^{2}}{(225+x^{2})^{2}}dx
limit as x approaches 0 of ((3^x-4^x))/x	\lim\:_{x\to\:0}(\frac{(3^{x}-4^{x})}{x})
maclaurin e^{9x}	maclaurin\:e^{9x}
derivative of 1/3 sin(3x)	derivative\:\frac{1}{3}\sin(3x)
12x^3-3y^2sqrt(x^4+1)y^'=0,y(0)=2	12x^{3}-3y^{2}\sqrt{x^{4}+1}y^{\prime\:}=0,y(0)=2
derivative of (cos(x))/(x^9)	derivative\:\frac{\cos(x)}{x^{9}}
integral of 1/(u^2-u)	\int\:\frac{1}{u^{2}-u}du
limit as x approaches-2 of (x^3-8)/(x-2)	\lim\:_{x\to\:-2}(\frac{x^{3}-8}{x-2})
(\partial)/(\partial y)(x^2+4y)	\frac{\partial\:}{\partial\:y}(x^{2}+4y)
slope of (7,-5),(-2,-5)	slope\:(7,-5),(-2,-5)
y=5^{6x^2}	y=5^{6x^{2}}
sum from n=2 to infinity of 1/((n+1)^2)	\sum\:_{n=2}^{\infty\:}\frac{1}{(n+1)^{2}}
derivative of v(t)=(4t^2+2)/(5t+5)	derivative\:v(t)=\frac{4t^{2}+2}{5t+5}
integral of (x+2)sqrt(2-x)	\int\:(x+2)\sqrt{2-x}dx
y^'=ky(1-y)	y^{\prime\:}=ky(1-y)
derivative of 1/x+ln(x)	\frac{d}{dx}(\frac{1}{x}+\ln(x))
tangent of 5x^2-x^3	tangent\:5x^{2}-x^{3}
f(x)= 1/(x^2+4)	f(x)=\frac{1}{x^{2}+4}
tangent of f(x)=(5x)/(x^2-4),\at x=3	tangent\:f(x)=\frac{5x}{x^{2}-4},\at\:x=3
limit as x approaches 6 of sqrt(x-6)	\lim\:_{x\to\:6}(\sqrt{x-6})
integral of-2tan(x)	\int\:-2\tan(x)dx
limit as x approaches+0 of (x^4)/(x^4)	\lim\:_{x\to\:+0}(\frac{x^{4}}{x^{4}})
integral of e^{5x}cos(4x)	\int\:e^{5x}\cos(4x)dx
derivative of f(x)=(e^{2x})/(1x+1)	derivative\:f(x)=\frac{e^{2x}}{1x+1}
derivative of (x^2-4/(x^2+2))	\frac{d}{dx}(\frac{x^{2}-4}{x^{2}+2})
tangent of e^x(5-4x+4x^2)	tangent\:e^{x}(5-4x+4x^{2})
(\partial)/(\partial x)(x^3e^{-2y})	\frac{\partial\:}{\partial\:x}(x^{3}e^{-2y})
y=(7sqrt(x)+4)x^2	y=(7\sqrt{x}+4)x^{2}
d/(dt)(s-t)	\frac{d}{dt}(s-t)
y^{''}-2y^'=8sin(2x)+2xe^{2x}	y^{\prime\:\prime\:}-2y^{\prime\:}=8\sin(2x)+2xe^{2x}
derivative of 9/x-2/(x^3+1/(x^4))	\frac{d}{dx}(\frac{9}{x}-\frac{2}{x^{3}}+\frac{1}{x^{4}})
(\partial)/(\partial x)(e^{xy}+1/(x+y))	\frac{\partial\:}{\partial\:x}(e^{xy}+\frac{1}{x+y})
tangent of 4x^2+2x-1	tangent\:4x^{2}+2x-1
f(x)=(5x^6+4x^3)^4	f(x)=(5x^{6}+4x^{3})^{4}
(\partial)/(\partial x)(ln(8x+7y))	\frac{\partial\:}{\partial\:x}(\ln(8x+7y))
y^{'''}-6y^{''}+11y^'-6y=xe^x	y^{\prime\:\prime\:\prime\:}-6y^{\prime\:\prime\:}+11y^{\prime\:}-6y=xe^{x}
integral from 1 to 5 of x/(x^2+6x+13)	\int\:_{1}^{5}\frac{x}{x^{2}+6x+13}dx
integral of 1/(1+e^{12x)}	\int\:\frac{1}{1+e^{12x}}dx
slope ofintercept (7,0),(-1,2)	slopeintercept\:(7,0),(-1,2)
derivative of e^{-(t-3)^2}	derivative\:e^{-(t-3)^{2}}
(\partial)/(\partial y)(x^3y^4)	\frac{\partial\:}{\partial\:y}(x^{3}y^{4})
d/(dy)(cos(x^2)-y)	\frac{d}{dy}(\cos(x^{2})-y)
integral from-4 to 6 of 6	\int\:_{-4}^{6}6dx
tangent of f(x)=-4x^2-4x+4,\at x=1	tangent\:f(x)=-4x^{2}-4x+4,\at\:x=1
tangent of-(12)/((4x+1)^2)	tangent\:-\frac{12}{(4x+1)^{2}}
integral of 1/((e^y+1)^2e^{-y)}	\int\:\frac{1}{(e^{y}+1)^{2}e^{-y}}dy

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