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Popular Calculus Problems

integral of (7/(x^2+1))	\int\:(\frac{7}{x^{2}+1})dx
derivative of csc^3(x^2)	\frac{d}{dx}(\csc^{3}(x^{2}))
derivative of (1+x^3^{2020})	\frac{d}{dx}((1+x^{3})^{2020})
derivative of 4e^{-x^2}	\frac{d}{dx}(4e^{-x^{2}})
slope of (8,8),(4,6)	slope\:(8,8),(4,6)
derivative of e^{2x}+2e^{2x}x	derivative\:e^{2x}+2e^{2x}x
(dy)/(dt)+ay=b	\frac{dy}{dt}+ay=b
tangent of 2sqrt(x)	tangent\:2\sqrt{x}
derivative of (x^4+36x^2)/((x^2+12)^2)	derivative\:\frac{x^{4}+36x^{2}}{(x^{2}+12)^{2}}
limit as x approaches 2 of e^{x^2-2x}	\lim\:_{x\to\:2}(e^{x^{2}-2x})
integral of x/(5x-4)	\int\:\frac{x}{5x-4}dx
integral of x(sqrt(a^2-x^2))	\int\:x(\sqrt{a^{2}-x^{2}})dx
derivative of f(x)= 1/2 x^2	derivative\:f(x)=\frac{1}{2}x^{2}
(\partial)/(\partial y)(ln(x^8y))	\frac{\partial\:}{\partial\:y}(\ln(x^{8}y))
(\partial)/(\partial x)(x^{1/4}*y^{3/4})	\frac{\partial\:}{\partial\:x}(x^{\frac{1}{4}}\cdot\:y^{\frac{3}{4}})
limit as x approaches pi-of 4x	\lim\:_{x\to\:π-}(4x)
(\partial)/(\partial x)(6x^{-3}-8x^{-5})	\frac{\partial\:}{\partial\:x}(6x^{-3}-8x^{-5})
derivative of 500x-(x^2/(ln(x+300)))	\frac{d}{dx}(500x-\frac{x^{2}}{\ln(x+300)})
derivative of (3x^2-6x+10(x^3))	\frac{d}{dx}((3x^{2}-6x+10)(x^{3}))
y^{''}+2y^'+5y=e^{(-x)}sec(2x)	y^{\prime\:\prime\:}+2y^{\prime\:}+5y=e^{(-x)}\sec(2x)
derivative of (12/(x^5)-7/(\sqrt[5]{x)})	\frac{d}{dx}(\frac{12}{x^{5}}-\frac{7}{\sqrt[5]{x}})
derivative of 4e^{5x}	derivative\:4e^{5x}
derivative of e^{x/y}ln((x^2/y))	\frac{d}{dx}(e^{\frac{x}{y}}\ln(\frac{x^{2}}{y}))
limit as x approaches 8 of 2	\lim\:_{x\to\:8}(2)
integral from 2 to 9 of 1/(x^2-1)	\int\:_{2}^{9}\frac{1}{x^{2}-1}dx
(xy-x)dx+(xy+y)dy=0	(xy-x)dx+(xy+y)dy=0
integral of xcos((npix)/3)	\int\:x\cos(\frac{nπx}{3})dx
integral of sin(r)	\int\:\sin(r)dr
tangent of y=9e^x+x	tangent\:y=9e^{x}+x
(dy)/(dx)=e^{2x-3y}	\frac{dy}{dx}=e^{2x-3y}
(\partial)/(\partial x)(7xcos(x)cos(y))	\frac{\partial\:}{\partial\:x}(7x\cos(x)\cos(y))
(dy)/(dt)=8-y/(200+3t)	\frac{dy}{dt}=8-\frac{y}{200+3t}
tangent of 7e^xcos(x)	tangent\:7e^{x}\cos(x)
tangent of f(x)=-2xe^{x^2},\at x=2	tangent\:f(x)=-2xe^{x^{2}},\at\:x=2
sum from n=4 to infinity of (x^n)/(n^5)	\sum\:_{n=4}^{\infty\:}\frac{x^{n}}{n^{5}}
derivative of sqrt(x-1)(x^2+1)	derivative\:\sqrt{x-1}(x^{2}+1)
limit as x approaches 0+of 6-1/(x^3)	\lim\:_{x\to\:0+}(6-\frac{1}{x^{3}})
t^2y^{''}-8ty^'+8y=0	t^{2}y^{\prime\:\prime\:}-8ty^{\prime\:}+8y=0
integral of 6xln(x)	\int\:6x\ln(x)dx
derivative of sin(t^2)	derivative\:\sin(t^{2})
integral of te^{-i2pift}	\int\:te^{-i2πft}dt
integral from 0 to pi of cos(3x)	\int\:_{0}^{π}\cos(3x)dx
y^{''}+4y^'+13y=0,y(0)=7,y^'(0)=7	y^{\prime\:\prime\:}+4y^{\prime\:}+13y=0,y(0)=7,y^{\prime\:}(0)=7
derivative of f(x)=(3x-4)	derivative\:f(x)=(3x-4)
derivative of 50sqrt(x)	\frac{d}{dx}(50\sqrt{x})
maclaurin ln(1+x^2)	maclaurin\:\ln(1+x^{2})
derivative of f(x)=e^2+ln(7)	derivative\:f(x)=e^{2}+\ln(7)
((1-cos(x))/x)^'	(\frac{1-\cos(x)}{x})^{\prime\:}
integral of (x-2)/(x^2+x+1)	\int\:\frac{x-2}{x^{2}+x+1}dx
derivative of-csc^2(x-cos(2x)*2)	\frac{d}{dx}(-\csc^{2}(x)-\cos(2x)\cdot\:2)
(y^2+1)dx=y(sec^2(x))dy	(y^{2}+1)dx=y(\sec^{2}(x))dy
derivative of (1-x(1+x^2)^{-1})	\frac{d}{dx}((1-x)(1+x^{2})^{-1})
integral of (9+sqrt(x)+x)/x	\int\:\frac{9+\sqrt{x}+x}{x}dx
sum from n=1 to infinity of arctan(19n)	\sum\:_{n=1}^{\infty\:}\arctan(19n)
integral of-4x^2sin(pix)	\int\:-4x^{2}\sin(πx)dx
tangent of f(x)=sqrt(5x+1),\at x=3	tangent\:f(x)=\sqrt{5x+1},\at\:x=3
(\partial)/(\partial x)(x-3y^2+4x^2y^3)	\frac{\partial\:}{\partial\:x}(x-3y^{2}+4x^{2}y^{3})
derivative of 4x^2+5	derivative\:4x^{2}+5
integral of (3x^2+2x)/(x^2-1)	\int\:\frac{3x^{2}+2x}{x^{2}-1}dx
derivative of e^x+ln(x)	\frac{d}{dx}(e^{x}+\ln(x))
y^{''}-4y^'=6t	y^{\prime\:\prime\:}-4y^{\prime\:}=6t
inverse oflaplace (7s^3-9s+1)/(3s^5)	inverselaplace\:\frac{7s^{3}-9s+1}{3s^{5}}
integral of 3/(x(x^4+1))	\int\:\frac{3}{x(x^{4}+1)}dx
(\partial)/(\partial z)(cos(xy))	\frac{\partial\:}{\partial\:z}(\cos(xy))
xyy^'-y^2=x^4	xyy^{\prime\:}-y^{2}=x^{4}
derivative of e^x*ln(x)	derivative\:e^{x}\cdot\:\ln(x)
taylor 1/(1+x^2)	taylor\:\frac{1}{1+x^{2}}
integral of 17e^{-17x}	\int\:17e^{-17x}dx
limit as x approaches 0 of x(1+1/x)	\lim\:_{x\to\:0}(x(1+\frac{1}{x}))
tangent of y=((x-1))/((x+1))	tangent\:y=\frac{(x-1)}{(x+1)}
(\partial)/(\partial y)(ln((xy)/(y^2+z^2)))	\frac{\partial\:}{\partial\:y}(\ln(\frac{xy}{y^{2}+z^{2}}))
(\partial)/(\partial y)(ye^{yx})	\frac{\partial\:}{\partial\:y}(ye^{yx})
derivative of 3cos(x)-2sin(x)	derivative\:3\cos(x)-2\sin(x)
integral of 3x^2+2	\int\:3x^{2}+2dx
limit as x approaches 0+of x-1	\lim\:_{x\to\:0+}(x-1)
area y=sqrt(5x),x=5	area\:y=\sqrt{5x},x=5
sum from n=1 to infinity of e^{-4n}	\sum\:_{n=1}^{\infty\:}e^{-4n}
(\partial)/(\partial y)(ln(x-7y))	\frac{\partial\:}{\partial\:y}(\ln(x-7y))
integral of 1/(sqrt(3-2x))	\int\:\frac{1}{\sqrt{3-2x}}dx
derivative of-(14/(x^3))	\frac{d}{dx}(-\frac{14}{x^{3}})
(11+x^2)y^'-2xy=0	(11+x^{2})y^{\prime\:}-2xy=0
integral of 1/(8x^2-16x+64)	\int\:\frac{1}{8x^{2}-16x+64}dx
(\partial)/(\partial t)(se^t)	\frac{\partial\:}{\partial\:t}(se^{t})
(\partial)/(\partial t)(ssin(t))	\frac{\partial\:}{\partial\:t}(s\sin(t))
limit as x approaches-2 of 5/(x+2)	\lim\:_{x\to\:-2}(\frac{5}{x+2})
f(x)=2^{3x^2-6}	f(x)=2^{3x^{2}-6}
tangent of f(x)=-6x^2-2x,\at x=3	tangent\:f(x)=-6x^{2}-2x,\at\:x=3
(dP)/(dt)=5sqrt(Pt),P(1)=3	\frac{dP}{dt}=5\sqrt{Pt},P(1)=3
derivative of x/(4.5c(c-x))	\frac{d}{dx}(\frac{x}{4.5c}(c-x))
integral from 0 to 1 of (x^2+1)^2	\int\:_{0}^{1}(x^{2}+1)^{2}dx
limit as t approaches 6 of 8(t-5)(t-7)	\lim\:_{t\to\:6}(8(t-5)(t-7))
derivative of (x+3/x /(sqrt(x)))	\frac{d}{dx}(\frac{x+\frac{3}{x}}{\sqrt{x}})
integral of (x^2+1)	\int\:(x^{2}+1)dx
integral of 2^{5x}	\int\:2^{5x}dx
tangent of y=x^2-7,(3,2)	tangent\:y=x^{2}-7,(3,2)
integral of e^{10x}	\int\:e^{10x}dx
(\partial)/(\partial y)(xy^3)	\frac{\partial\:}{\partial\:y}(xy^{3})
(\partial)/(\partial x)(xy^4)	\frac{\partial\:}{\partial\:x}(xy^{4})
integral of ((2x^2+9x+2))/((x^2+1)^2)	\int\:\frac{(2x^{2}+9x+2)}{(x^{2}+1)^{2}}dx
integral of (2x+1)/(sqrt(x^2-1))	\int\:\frac{2x+1}{\sqrt{x^{2}-1}}dx

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