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Popular Calculus Problems

derivative of cos(θx)	\frac{d}{dx}(\cos(θ)x)
integral of sqrt(5x)	\int\:\sqrt{5x}dx
derivative of xy^3-x^2	\frac{d}{dx}(xy^{3}-x^{2})
derivative of f(x)=2(x^3-x)^4	derivative\:f(x)=2(x^{3}-x)^{4}
(\partial)/(\partial y)(sin^2(xy))	\frac{\partial\:}{\partial\:y}(\sin^{2}(xy))
y^'+(4y)/x =-3/x ,y(1)=-2	y^{\prime\:}+\frac{4y}{x}=-\frac{3}{x},y(1)=-2
integral of-2cos(x/2)	\int\:-2\cos(\frac{x}{2})dx
limit as x approaches 2 of x^2+3x	\lim\:_{x\to\:2}(x^{2}+3x)
integral of 9x^{-2}	\int\:9x^{-2}dx
derivative of (x-2/(x+2))	\frac{d}{dx}(\frac{x-2}{x+2})
derivative of y=xe^{ax}	derivative\:y=xe^{ax}
derivative of (x^4/2-3/2 x^2-x)	\frac{d}{dx}(\frac{x^{4}}{2}-\frac{3}{2}x^{2}-x)
limit as x approaches-2 of x^2-5	\lim\:_{x\to\:-2}(x^{2}-5)
integral from 1 to infinity of x^{-4/5}	\int\:_{1}^{\infty\:}x^{-\frac{4}{5}}dx
f^'(x)=6x	f^{\prime\:}(x)=6x
derivative of f(x)= 2/(3x)	derivative\:f(x)=\frac{2}{3x}
derivative of (3x^2/(x^2-4))	\frac{d}{dx}(\frac{3x^{2}}{x^{2}-4})
(dy)/(dx)=cos(x-y)	\frac{dy}{dx}=\cos(x-y)
sum from n=0 to infinity of (n+6)/6	\sum\:_{n=0}^{\infty\:}\frac{n+6}{6}
(\partial)/(\partial x)(e^{x^2y^3})	\frac{\partial\:}{\partial\:x}(e^{x^{2}y^{3}})
derivative of 12e^2x	\frac{d}{dx}(12e^{2}x)
(\partial)/(\partial x)(y^2zcos(x))	\frac{\partial\:}{\partial\:x}(y^{2}z\cos(x))
(\partial}{\partial x}(\frac{x^3y^3)/3)	\frac{\partial\:}{\partial\:x}(\frac{x^{3}y^{3}}{3})
(\partial}{\partial x}(\frac{g(x))/x-(h(x))/x)	\frac{\partial\:}{\partial\:x}(\frac{g(x)}{x}-\frac{h(x)}{x})
integral of sec^7(x)tan(x)	\int\:\sec^{7}(x)\tan(x)dx
integral of e^{tan(v)}sec^2(v)	\int\:e^{\tan(v)}\sec^{2}(v)dv
derivative of (e^{-t^2}x^2)	\frac{d}{dx}((e^{-t^{2}})x^{2})
integral of (xe^{x^2})/(sqrt(e^{x^2)+2)}	\int\:\frac{xe^{x^{2}}}{\sqrt{e^{x^{2}}+2}}dx
limit as n approaches infinity+of 1^n	\lim\:_{n\to\:\infty\:+}(1^{n})
limit as x approaches-2 of (x^3-1)/(x-1)	\lim\:_{x\to\:-2}(\frac{x^{3}-1}{x-1})
y^{''}+8y+16y=0	y^{\prime\:\prime\:}+8y+16y=0
sum from n=1 to infinity of ne^{9n}	\sum\:_{n=1}^{\infty\:}ne^{9n}
integral of (x+1)^{-1}	\int\:(x+1)^{-1}dx
area sqrt(x+3),(x+3)/2	area\:\sqrt{x+3},\frac{x+3}{2}
(dy}{dx}=\frac{5y)/x	\frac{dy}{dx}=\frac{5y}{x}
derivative of (ln(x)/(x^{12)})	\frac{d}{dx}(\frac{\ln(x)}{x^{12}})
integral of sec^4(x)*tan^2(x)	\int\:\sec^{4}(x)\cdot\:\tan^{2}(x)dx
integral from 0 to 3 of x^2-3x	\int\:_{0}^{3}x^{2}-3xdx
derivative of ln((x+1/(x^2+1)))	\frac{d}{dx}(\ln(\frac{x+1}{x^{2}+1}))
integral from 1 to 8 of 9(ln(x))/(x^2)	\int\:_{1}^{8}9\frac{\ln(x)}{x^{2}}dx
taylor x^{x^2},1	taylor\:x^{x^{2}},1
derivative of 1/(xsqrt(x^2-1))	derivative\:\frac{1}{x\sqrt{x^{2}-1}}
(\partial)/(\partial x)(7cos(x)sin(y))	\frac{\partial\:}{\partial\:x}(7\cos(x)\sin(y))
derivative of (e^{3x}/x)	\frac{d}{dx}(\frac{e^{3x}}{x})
derivative of ln(8-4x)	\frac{d}{dx}(\ln(8-4x))
derivative of cos(sqrt(x)+e^x)	\frac{d}{dx}(\cos(\sqrt{x}+e^{x}))
derivative of (x^2+4/(5x-9))	\frac{d}{dx}(\frac{x^{2}+4}{5x-9})
y^{''}-4y^'+3y=0,y(0)=-7.5,y^'(0)= 23/5	y^{\prime\:\prime\:}-4y^{\prime\:}+3y=0,y(0)=-7.5,y^{\prime\:}(0)=\frac{23}{5}
derivative of f(x)=sqrt(3)	derivative\:f(x)=\sqrt{3}
limit as x approaches 9-of 2/(x-9)	\lim\:_{x\to\:9-}(\frac{2}{x-9})
integral of tan^4(8x)	\int\:\tan^{4}(8x)dx
integral of 1/(sqrt(v^2+1))	\int\:\frac{1}{\sqrt{v^{2}+1}}dv
derivative of y=1-x-x^2	derivative\:y=1-x-x^{2}
integral of (x^4)/4+cosh(x)+C	\int\:\frac{x^{4}}{4}+\cosh(x)+Cdx
derivative of y=sqrt(e^2+2x)	derivative\:y=\sqrt{e^{2}+2x}
limit as x approaches 0 of (e^x-1)/(15x)	\lim\:_{x\to\:0}(\frac{e^{x}-1}{15x})
derivative of (e^{ax}-e^{-ax}/(e^{ax)+e^{-ax}})	\frac{d}{dx}(\frac{e^{ax}-e^{-ax}}{e^{ax}+e^{-ax}})
integral of 2xe^2x	\int\:2xe^{2}xdx
limit as x approaches 1 of sqrt(5-x)	\lim\:_{x\to\:1}(\sqrt{5-x})
integral from 6 to 8 of (100)/((x-6)^3)	\int\:_{6}^{8}\frac{100}{(x-6)^{3}}dx
derivative of 5/((x+1^2))	\frac{d}{dx}(\frac{5}{(x+1)^{2}})
integral of (e^{5x}+e^{-5x})^2	\int\:(e^{5x}+e^{-5x})^{2}dx
integral of (2^{x+1}-3^{x+1})/(2^{x+1)}	\int\:\frac{2^{x+1}-3^{x+1}}{2^{x+1}}dx
integral of (1-4x^2)	\int\:(1-4x^{2})dx
derivative of (2x-3^{ln(x)})	\frac{d}{dx}((2x-3)^{\ln(x)})
derivative of x^3y-2x^2+y^4	\frac{d}{dx}(x^{3}y-2x^{2}+y^{4})
integral of e^{-y/x}	\int\:e^{-\frac{y}{x}}dy
integral of (sin(x))/(1-sin^2(x))	\int\:\frac{\sin(x)}{1-\sin^{2}(x)}dx
f(x)=(1-cos(x))/x	f(x)=\frac{1-\cos(x)}{x}
integral from 0 to 4 of x/2	\int\:_{0}^{4}\frac{x}{2}dx
(1-x^2)y^'-xy=1	(1-x^{2})y^{\prime\:}-xy=1
tangent of (2x)/(x^2-7)	tangent\:\frac{2x}{x^{2}-7}
y^'+6y=3	y^{\prime\:}+6y=3
derivative of cos(x-cos(2x))	\frac{d}{dx}(\cos(x)-\cos(2x))
derivative of f(x)=sqrt(x/(x+1))	derivative\:f(x)=\sqrt{\frac{x}{x+1}}
integral of 3x^2-x^3	\int\:3x^{2}-x^{3}dx
limit as x approaches 1 of sqrt(x+8)	\lim\:_{x\to\:1}(\sqrt{x+8})
integral of sec^2(x)tan^9(x)	\int\:\sec^{2}(x)\tan^{9}(x)dx
(d^2)/(dx^2)((x^3)/(x^2-1))	\frac{d^{2}}{dx^{2}}(\frac{x^{3}}{x^{2}-1})
sum from n=1 to infinity of 1/(3^n-5)	\sum\:_{n=1}^{\infty\:}\frac{1}{3^{n}-5}
derivative of 2+3/(1+(x+1)^2)	derivative\:2+\frac{3}{1+(x+1)^{2}}
d/(da)(cos(a)sin(a))	\frac{d}{da}(\cos(a)\sin(a))
derivative of-5xy(x+y+6)	\frac{d}{dx}(-5xy(x+y)+6)
(\partial)/(\partial x)(x/a)	\frac{\partial\:}{\partial\:x}(\frac{x}{a})
integral of-(25)/(x^{26)}	\int\:-\frac{25}{x^{26}}dx
t^2y^'+ty=7	t^{2}\cdot\:y^{\prime\:}+t\cdot\:y=7
integral of x^3cos(x^4)	\int\:x^{3}\cos(x^{4})dx
(\partial)/(\partial x)(cos(e^{-x^2}))	\frac{\partial\:}{\partial\:x}(\cos(e^{-x^{2}}))
derivative of x^{10}-1	\frac{d}{dx}(x^{10}-1)
derivative of 4x^2-x^3	\frac{d}{dx}(4x^{2}-x^{3})
integral of 4sqrt(x)	\int\:4\sqrt{x}dx
integral of 6x^{-3}	\int\:6x^{-3}dx
integral of x^4sqrt(1-x^2)	\int\:x^{4}\sqrt{1-x^{2}}dx
f(x)=x^7	f(x)=x^{7}
integral of (9x-27)/((x^2+2x+4)^2)	\int\:\frac{9x-27}{(x^{2}+2x+4)^{2}}dx
integral from 0 to 5 of x/(x+10)	\int\:_{0}^{5}\frac{x}{x+10}dx
integral of (x^2+1)x	\int\:(x^{2}+1)xdx
derivative of ((d^2y))/((dx^2))	derivative\:\frac{(d^{2}y)}{(dx^{2})}
derivative of y=(2x^3+7)^2	derivative\:y=(2x^{3}+7)^{2}
laplacetransform (t-2)e^t	laplacetransform\:(t-2)e^{t}

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