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Popular Calculus Problems

(dy)/(dx)+2y=3,y(0)=1	\frac{dy}{dx}+2y=3,y(0)=1
derivative of f(x)=x^4+8x	derivative\:f(x)=x^{4}+8x
derivative of ({g}(x)/(h(x)))	\frac{d}{dx}(\frac{{g}(x)}{h(x)})
derivative of f(x)=4x-8	derivative\:f(x)=4x-8
integral of 9xcos(3x)	\int\:9x\cos(3x)dx
integral of e^{-x}*cos(2x)	\int\:e^{-x}\cdot\:\cos(2x)dx
derivative of-sin(x)	\frac{d}{dx}(-\sin(x))
sum from n=1 to infinity of (n^4)/(n!)	\sum\:_{n=1}^{\infty\:}\frac{n^{4}}{n!}
integral from 0 to 9 of 1/3 x-2	\int\:_{0}^{9}\frac{1}{3}x-2dx
integral of (4-4x)/(1-sqrt(x))	\int\:\frac{4-4x}{1-\sqrt{x}}dx
derivative of (5x^4+2(3sin(x)))	\frac{d}{dx}((5x^{4}+2)(3\sin(x)))
derivative of 8/(x^4)	derivative\:\frac{8}{x^{4}}
derivative of e^{-8x}sin(8x)	\frac{d}{dx}(e^{-8x}\sin(8x))
integral of 3e^t	\int\:3e^{t}dt
limit as x approaches-2-of 3/(x+2)	\lim\:_{x\to\:-2-}(\frac{3}{x+2})
derivative of (1-x/(e^{2x)})	\frac{d}{dx}(\frac{1-x}{e^{2x}})
integral from 0 to 2pi of 9x^2sin(1/4 x)	\int\:_{0}^{2π}9x^{2}\sin(\frac{1}{4}x)dx
integral of sin(3)(x)cos(x)	\int\:\sin(3)(x)\cos(x)dx
limit as x approaches pi of x/(sin(x))	\lim\:_{x\to\:π}(\frac{x}{\sin(x)})
derivative of (ax^3+x^2+2/(1+x+x^2))	\frac{d}{dx}(\frac{ax^{3}+x^{2}+2}{1+x+x^{2}})
tangent of y=5e^xcos(x),(0,5)	tangent\:y=5e^{x}\cos(x),(0,5)
derivative of y=xln^3(x)	derivative\:y=x\ln^{3}(x)
(\partial)/(\partial x)(x-x^2y-y+xy^2)	\frac{\partial\:}{\partial\:x}(x-x^{2}y-y+xy^{2})
limit as x approaches 0 of x^7sin(1/x)	\lim\:_{x\to\:0}(x^{7}\sin(\frac{1}{x}))
derivative of (9-x/9)^{-7}	derivative\:(9-\frac{x}{9})^{-7}
area x=-2,x=1,y=7x,y=x^2-8	area\:x=-2,x=1,y=7x,y=x^{2}-8
implicit (dy)/(dx),6x^2+3xy+2y^2+17y-6=0	implicit\:\frac{dy}{dx},6x^{2}+3xy+2y^{2}+17y-6=0
y^{''}-7y^'+12y=0	y^{\prime\:\prime\:}-7y^{\prime\:}+12y=0
derivative of 2x+1	derivative\:2x+1
y^{''}-3y^'+18y=0	y^{\prime\:\prime\:}-3y^{\prime\:}+18y=0
integral of (x-2)(x-3)^6	\int\:(x-2)(x-3)^{6}dx
(\partial)/(\partial x)(4(x-y)e^{4y+2x^2})	\frac{\partial\:}{\partial\:x}(4(x-y)e^{4y+2x^{2}})
derivative of f(x)=x^3-1	derivative\:f(x)=x^{3}-1
(\partial)/(\partial x)(4x^3-5x^2+8x)	\frac{\partial\:}{\partial\:x}(4x^{3}-5x^{2}+8x)
y^'=(2x+y)/(2x+y+3)	y^{\prime\:}=\frac{2x+y}{2x+y+3}
integral of sin^2(5x)	\int\:\sin^{2}(5x)dx
derivative of 4e^x+8/(\sqrt[3]{x)}	derivative\:4e^{x}+\frac{8}{\sqrt[3]{x}}
(\partial)/(\partial x)(5sqrt(x^2+y^2))	\frac{\partial\:}{\partial\:x}(5\sqrt{x^{2}+y^{2}})
(dy)/(dx)=(y^2-1)/(x^2-1),y(5)=5	\frac{dy}{dx}=\frac{y^{2}-1}{x^{2}-1},y(5)=5
derivative of (3x-2^5)	\frac{d}{dx}((3x-2)^{5})
integral of 4e^xsqrt(8+e^x)	\int\:4e^{x}\sqrt{8+e^{x}}dx
limit as x approaches 6 of x+3	\lim\:_{x\to\:6}(x+3)
(arctan(e^x))^'	(\arctan(e^{x}))^{\prime\:}
derivative of arccsc(2x+1)	\frac{d}{dx}(\arccsc(2x+1))
integral of (sin(x))^3(cos(x))	\int\:(\sin(x))^{3}(\cos(x))dx
limit as x approaches-1 of 1/(x+1)	\lim\:_{x\to\:-1}(\frac{1}{x+1})
limit as x approaches 0 of e^{7x}	\lim\:_{x\to\:0}(e^{7x})
integral of arccos(7x)	\int\:\arccos(7x)dx
sum from n=0 to infinity of n+2	\sum\:_{n=0}^{\infty\:}n+2
(dx)/(dt)=-2x-3x^2	\frac{dx}{dt}=-2x-3x^{2}
derivative of (cos^2(s)-4s^2)^2	derivative\:(\cos^{2}(s)-4s^{2})^{2}
integral of e^{4x}cos(9x)	\int\:e^{4x}\cos(9x)dx
integral from-2pi to 2pi of (sin^2(x)+1)	\int\:_{-2π}^{2π}(\sin^{2}(x)+1)dx
integral of log_{e}(5x)	\int\:\log_{e}(5x)dx
f(x)=-2sin(x)	f(x)=-2\sin(x)
derivative of sqrt(300-3p)	derivative\:\sqrt{300-3p}
(\partial)/(\partial x)(arcsin(y))	\frac{\partial\:}{\partial\:x}(\arcsin(y))
integral of x/(1+cos(2x))	\int\:\frac{x}{1+\cos(2x)}dx
derivative of arcsin(3x)	derivative\:\arcsin(3x)
integral of (x^2-x+6)/(x(x^2+3))	\int\:\frac{x^{2}-x+6}{x(x^{2}+3)}dx
y^{''}-(y^')^2=0	y^{\prime\:\prime\:}-(y^{\prime\:})^{2}=0
roots (ax+b)/(cx+d)	roots\:\frac{ax+b}{cx+d}
derivative of 3x^6	\frac{d}{dx}(3x^{6})
limit as x approaches 0-of (23)/(tan(x))	\lim\:_{x\to\:0-}(\frac{23}{\tan(x)})
tangent of f(x)= 6/(x+1)	tangent\:f(x)=\frac{6}{x+1}
limit as x approaches+1+of 7/(1-x)	\lim\:_{x\to\:+1+}(\frac{7}{1-x})
integral of (27)/(x^2)	\int\:\frac{27}{x^{2}}dx
integral of 2/(x(x-2)^2)	\int\:\frac{2}{x(x-2)^{2}}dx
derivative of x^3cos(y)	\frac{d}{dx}(x^{3}\cos(y))
derivative of ((x^2-1))/(2x-3)	derivative\:\frac{(x^{2}-1)}{2x-3}
(\partial)/(\partial y)(4x^3y^3+3)	\frac{\partial\:}{\partial\:y}(4x^{3}y^{3}+3)
derivative of sqrt(4x+5)	\frac{d}{dx}(\sqrt{4x+5})
integral of sin^3(4x)cos^{-2}(4x)	\int\:\sin^{3}(4x)\cos^{-2}(4x)dx
integral of cot^7(x/2)csc^2(x/2)	\int\:\cot^{7}(\frac{x}{2})\csc^{2}(\frac{x}{2})dx
slope of (-2,-9),(0,-3)	slope\:(-2,-9),(0,-3)
derivative of (x-3^3)	\frac{d}{dx}((x-3)^{3})
y^'=(3x^2-1)/(3+2y)	y^{\prime\:}=\frac{3x^{2}-1}{3+2y}
derivative of axsin(kx+bxcos(kx))	\frac{d}{dx}(ax\sin(kx)+bx\cos(kx))
derivative of f(x)=5x+2	derivative\:f(x)=5x+2
derivative of f(x)=-2ln(x)+x^2-4+e^x+x^e	derivative\:f(x)=-2\ln(x)+x^{2}-4+e^{x}+x^{e}
derivative of 2^{ln(x})	\frac{d}{dx}(2^{\ln(x)})
(d^3)/(dx^3)(2x^3-4)	\frac{d^{3}}{dx^{3}}(2x^{3}-4)
(\partial)/(\partial x)(e^{-2x}cos(9pit))	\frac{\partial\:}{\partial\:x}(e^{-2x}\cos(9πt))
integral from 0 to pi of 7sin^2(4x)	\int\:_{0}^{π}7\sin^{2}(4x)dx
d/(dt)(2cos(2t))	\frac{d}{dt}(2\cos(2t))
derivative of x/(5x+8)	\frac{d}{dx}(\frac{x}{5x+8})
limit as x approaches-2+of (1-x)/(x+2)	\lim\:_{x\to\:-2+}(\frac{1-x}{x+2})
(\partial)/(\partial x)(x^5)	\frac{\partial\:}{\partial\:x}(x^{5})
integral of cos(4x)sin^5(4x)	\int\:\cos(4x)\sin^{5}(4x)dx
derivative of f(x)=(x^2)/(x-1)	derivative\:f(x)=\frac{x^{2}}{x-1}
tangent of 4(8x-1)^4	tangent\:4(8x-1)^{4}
x^{''}+4x^'+4x=e^{-2t}	x^{\prime\:\prime\:}+4x^{\prime\:}+4x=e^{-2t}
derivative of f(x)=3sqrt(x^3)	derivative\:f(x)=3\sqrt{x^{3}}
integral from 0 to 8 of-x^2+2x+4	\int\:_{0}^{8}-x^{2}+2x+4dx
tangent of f(x)=(4x)/(x+1),\at x=3	tangent\:f(x)=\frac{4x}{x+1},\at\:x=3
limit as x approaches-4 of (\|x+4\|)/(x+4)	\lim\:_{x\to\:-4}(\frac{\left\|x+4\right\|}{x+4})
derivative of y=(e^{4x}-3)^8	derivative\:y=(e^{4x}-3)^{8}
(d^3)/(dx^3)(2x^3-4x^2+2)	\frac{d^{3}}{dx^{3}}(2x^{3}-4x^{2}+2)
area x^3-5x,4x	area\:x^{3}-5x,4x
derivative of 7/(x+4)	\frac{d}{dx}(\frac{7}{x+4})

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