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Popular Calculus Problems

y'=0.027y(1-y/(1527))	y\prime\:=0.027y(1-\frac{y}{1527})
derivative of ln(3)+e^{x^e}	derivative\:\ln(3)+e^{x^{e}}
y^{''}-5y^'=10x+3	y^{\prime\:\prime\:}-5y^{\prime\:}=10x+3
xyy^'+x^2+y^2=0	xyy^{\prime\:}+x^{2}+y^{2}=0
integral of (5x^4+6)/(x^5+6x)	\int\:\frac{5x^{4}+6}{x^{5}+6x}dx
limit as x approaches 5+of 4/(x-5)	\lim\:_{x\to\:5+}(\frac{4}{x-5})
limit as x approaches 0 of x^8-1/x	\lim\:_{x\to\:0}(x^{8}-\frac{1}{x})
derivative of sin^3(2x-cos(2x))	\frac{d}{dx}(\sin^{3}(2x)-\cos(2x))
integral of e^{-v}sin(wv)	\int\:e^{-v}\sin(wv)dv
(dy)/(dt)=-t/y ,y(0)=4	\frac{dy}{dt}=-\frac{t}{y},y(0)=4
derivative of (x^2+2x/(1-x^2))	\frac{d}{dx}(\frac{x^{2}+2x}{1-x^{2}})
tangent of x^4+6x^2-x	tangent\:x^{4}+6x^{2}-x
integral of (sin(y))/(cos(y))	\int\:\frac{\sin(y)}{\cos(y)}dy
(\partial)/(\partial y)(-e^{-x}sin(y))	\frac{\partial\:}{\partial\:y}(-e^{-x}\sin(y))
(\partial)/(\partial y)(4x^2+4xy-3y^2+4y-1)	\frac{\partial\:}{\partial\:y}(4x^{2}+4xy-3y^{2}+4y-1)
limit as x approaches 1 of x-1	\lim\:_{x\to\:1}(x-1)
integral of sec^2(x)+sec(2x)tan(2x)	\int\:\sec^{2}(x)+\sec(2x)\tan(2x)dx
derivative of p(θ)=sqrt(7θ)	derivative\:p(θ)=\sqrt{7θ}
f(x)=ln(x+4)	f(x)=\ln(x+4)
integral of 1/(2sin(x)-3cos(x)-5)	\int\:\frac{1}{2\sin(x)-3\cos(x)-5}dx
limit as x approaches infinity of 0/0	\lim\:_{x\to\:\infty\:}(\frac{0}{0})
inverse oflaplace (s+3)/((s+1)^2)	inverselaplace\:\frac{s+3}{(s+1)^{2}}
(dy)/(dt)=-4(y-2)	\frac{dy}{dt}=-4(y-2)
d/(dy)(6y)	\frac{d}{dy}(6y)
derivative of y=ln(sqrt((a+bx)/(a-bx)))	derivative\:y=\ln(\sqrt{\frac{a+bx}{a-bx}})
taylor cos(x+1)	taylor\:\cos(x+1)
(\partial)/(\partial x)(12y^5x^3+35y^8x^6)	\frac{\partial\:}{\partial\:x}(12y^{5}x^{3}+35y^{8}x^{6})
6(t+1)(dy)/(dt)-5y=5t	6(t+1)\frac{dy}{dt}-5y=5t
limit as x approaches 0 of ((x^2-2))/x	\lim\:_{x\to\:0}(\frac{(x^{2}-2)}{x})
d/(d{x)}({x}^4+{y}^4+{z}^4-4{x}{y}{z})	\frac{d}{d{x}}({x}^{4}+{y}^{4}+{z}^{4}-4{x}{y}{z})
integral of x/(x-3)	\int\:\frac{x}{x-3}dx
derivative of-x^3+x	\frac{d}{dx}(-x^{3}+x)
area 4cos(7x),4-4cos(7x),0, pi/7	area\:4\cos(7x),4-4\cos(7x),0,\frac{π}{7}
inverse oflaplace ((s+1))/(s^2+1)	inverselaplace\:\frac{(s+1)}{s^{2}+1}
derivative of 9/x	derivative\:\frac{9}{x}
limit as x approaches 0-of 3^{1/x}	\lim\:_{x\to\:0-}(3^{\frac{1}{x}})
integral of (x^2)/(xsqrt(x^2-x+1))	\int\:\frac{x^{2}}{x\sqrt{x^{2}-x+1}}dx
integral of xcos(1/2 x)	\int\:x\cos(\frac{1}{2}x)dx
y^{''}+3y^'+2y=x+6e^x,y(0)=0,y^'(0)=1	y^{\prime\:\prime\:}+3y^{\prime\:}+2y=x+6e^{x},y(0)=0,y^{\prime\:}(0)=1
tangent of y=sin(xy)+pi,(1,pi)	tangent\:y=\sin(xy)+π,(1,π)
7(d^2y)/(dx^2)+4(dy)/(dx)+9y=0	7\frac{d^{2}y}{dx^{2}}+4\frac{dy}{dx}+9y=0
tangent of f(x)=x^4+3x^2-x,(1,3)	tangent\:f(x)=x^{4}+3x^{2}-x,(1,3)
integral from 0 to a of x	\int\:_{0}^{a}xdx
integral from 0 to 1 of 6x^2+4x-3+4e^{4x}	\int\:_{0}^{1}6x^{2}+4x-3+4e^{4x}dx
y^{''}-5y^'+6y=2e^t	y^{\prime\:\prime\:}-5y^{\prime\:}+6y=2e^{t}
slope of (5,2),(2,-3)	slope\:(5,2),(2,-3)
derivative of x/(x^4+1)	\frac{d}{dx}(\frac{x}{x^{4}+1})
tangent of y=(x^3-16x)^{14},(4,0)	tangent\:y=(x^{3}-16x)^{14},(4,0)
derivative of 1/(\sqrt[3]{(5-x^3)^5)}	derivative\:\frac{1}{\sqrt[3]{(5-x^{3})^{5}}}
y^'+4xy=x^3e^{x^2},y(0)=-1	y^{\prime\:}+4xy=x^{3}e^{x^{2}},y(0)=-1
integral of xcosh(2x^2-3)	\int\:x\cosh(2x^{2}-3)dx
inverse oflaplace (e^{-s})/((s+1)^2+1)	inverselaplace\:\frac{e^{-s}}{(s+1)^{2}+1}
integral from 0 to pi of 2sin^4(x)	\int\:_{0}^{π}2\sin^{4}(x)dx
integral of (x^3)/(x^2+x+1)	\int\:\frac{x^{3}}{x^{2}+x+1}dx
x^2y^{''}-7xy^'-20y=0	x^{2}y^{\prime\:\prime\:}-7xy^{\prime\:}-20y=0
y^{''}+9y=30sin(t)	y^{\prime\:\prime\:}+9y=30\sin(t)
derivative of f(x)=e^xsqrt(x)	derivative\:f(x)=e^{x}\sqrt{x}
area y=8cos(3x),y=8sin(3x),(0, pi/(12))	area\:y=8\cos(3x),y=8\sin(3x),(0,\frac{π}{12})
tangent of f(x)= 5/(sqrt(x)),(1,5)	tangent\:f(x)=\frac{5}{\sqrt{x}},(1,5)
derivative of (x^2+x^3^4)	\frac{d}{dx}((x^{2}+x^{3})^{4})
(\partial)/(\partial x)(xy^2e^z)	\frac{\partial\:}{\partial\:x}(x\cdot\:y^{2}\cdot\:e^{z})
derivative of y=cos^3(pit-16)	derivative\:y=\cos^{3}(πt-16)
tangent of f(x)=x^4+2x^2-x,(1,2)	tangent\:f(x)=x^{4}+2x^{2}-x,(1,2)
derivative of x,x^2-y,x+y^2	\frac{d}{dx}(x,x^{2}-y,x+y^{2})
integral of 5/((8z-1)^{7/8)}	\int\:\frac{5}{(8z-1)^{\frac{7}{8}}}dz
derivative of e^2+ln(4)	derivative\:e^{2}+\ln(4)
limit as x approaches 0-of 1/x	\lim\:_{x\to\:0-}(\frac{1}{x})
limit as x approaches 2 of (x-2)/(4-x^2)	\lim\:_{x\to\:2}(\frac{x-2}{4-x^{2}})
(\partial}{\partial x}(\frac{x^2-y^2)/2)	\frac{\partial\:}{\partial\:x}(\frac{x^{2}-y^{2}}{2})
(\partial)/(\partial x)(1/((x+3y)))	\frac{\partial\:}{\partial\:x}(\frac{1}{(x+3y)})
derivative of 9/(4(1+x^{5/2)})	\frac{d}{dx}(\frac{9}{4(1+x)^{\frac{5}{2}}})
integral of x/(sqrt(3-x^4))	\int\:\frac{x}{\sqrt{3-x^{4}}}dx
derivative of (x^{3/2})/3-x^{1/2}	derivative\:\frac{x^{\frac{3}{2}}}{3}-x^{\frac{1}{2}}
derivative of {f}(x*e^{1/({f)(x)}})	\frac{d}{dx}({f}(x)\cdot\:e^{\frac{1}{{f}(x)}})
derivative of 6(x+2)^{1/2}	derivative\:6(x+2)^{\frac{1}{2}}
integral from 0 to 6 of x^2sqrt(36-x^2)	\int\:_{0}^{6}x^{2}\sqrt{36-x^{2}}dx
y=(3x^5-7x^2-4)/(x^2)	y=\frac{3x^{5}-7x^{2}-4}{x^{2}}
derivative of 4^{e^x}	\frac{d}{dx}(4^{e^{x}})
derivative of e^{-,\at}	derivative\:e^{-,\at\:}
y^{''}+4y=3sec(2x)	y^{\prime\:\prime\:}+4y=3\sec(2x)
derivative of (3x^2+1)(2x+2)^2	derivative\:(3x^{2}+1)(2x+2)^{2}
integral of ((x+5))/((x+3)(x-2)^2)	\int\:\frac{(x+5)}{(x+3)(x-2)^{2}}dx
(\partial)/(\partial x)(e^x+sin(y))	\frac{\partial\:}{\partial\:x}(e^{x}+\sin(y))
limit as x approaches 0+of ln(sinh(x))	\lim\:_{x\to\:0+}(\ln(\sinh(x)))
derivative of-2sin(x-x)	\frac{d}{dx}(-2\sin(x)-x)
f(x)=x+sin(x)	f(x)=x+\sin(x)
derivative of (89t)/(99t-89)	derivative\:\frac{89t}{99t-89}
integral from 0 to 5 of 1/(x^2)	\int\:_{0}^{5}\frac{1}{x^{2}}dx
limit as x approaches pi/2 of 9sin(x)	\lim\:_{x\to\:\frac{π}{2}}(9\sin(x))
derivative of log_{e}(7x^2)	derivative\:\log_{e}(7x^{2})
derivative of x^{sin(x})	\frac{d}{dx}(x^{\sin(x)})
limit as h approaches 0 of (ln(1+h))/h	\lim\:_{h\to\:0}(\frac{\ln(1+h)}{h})
maclaurin e^{-3x}	maclaurin\:e^{-3x}
(f(x)(x^2))'	(f(x)(x^{2}))\prime\:
f(x)=(sin(sqrt(x)))/(cos(ln(-x)))	f(x)=\frac{\sin(\sqrt{x})}{\cos(\ln(-x))}
slope of xy-4y^2=8	slope\:xy-4y^{2}=8
integral of \sqrt[5]{x^3}	\int\:\sqrt[5]{x^{3}}dx
integral of ((2t^2+tsqrt(t)-1))/(t^2)	\int\:\frac{(2t^{2}+t\sqrt{t}-1)}{t^{2}}dt
integral of 1/(sin(y)+1)	\int\:\frac{1}{\sin(y)+1}dy
area y=x^3,x=y^2-2	area\:y=x^{3},x=y^{2}-2

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