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Popular Calculus Problems

(\partial)/(\partial x)(9(x+y)^2)	\frac{\partial\:}{\partial\:x}(9(x+y)^{2})
integral of 20cos(10t+pi/6)	\int\:20\cos(10t+\frac{π}{6})dt
limit as x approaches pi of-7sin(-x/2)	\lim\:_{x\to\:π}(-7\sin(-\frac{x}{2}))
integral from 0 to 1 of xcos(npix)	\int\:_{0}^{1}x\cos(nπx)dx
derivative of (x^4+36x^2/((x^2+12)^2))	\frac{d}{dx}(\frac{x^{4}+36x^{2}}{(x^{2}+12)^{2}})
derivative of y=(e^{9x}+e^{-9x})/x	derivative\:y=\frac{e^{9x}+e^{-9x}}{x}
integral of tan^2(4x)	\int\:\tan^{2}(4x)dx
integral of xsqrt(x)	\int\:x\sqrt{x}dx
integral from-infinity to 3 of e^{0.0001t}	\int\:_{-\infty\:}^{3}e^{0.0001t}dt
(\partial)/(\partial y)(x/y)	\frac{\partial\:}{\partial\:y}(\frac{x}{y})
derivative of e^{ax^8}	\frac{d}{dx}(e^{ax^{8}})
tangent of f(x)=-(4x)/(x^2+1),\at x=-1	tangent\:f(x)=-\frac{4x}{x^{2}+1},\at\:x=-1
limit as t approaches 0 of (t^3-3t)/t	\lim\:_{t\to\:0}(\frac{t^{3}-3t}{t})
derivative of (4x-3^3)	\frac{d}{dx}((4x-3)^{3})
(\partial)/(\partial y)(10x^{1/4}y^{3/4})	\frac{\partial\:}{\partial\:y}(10x^{\frac{1}{4}}y^{\frac{3}{4}})
sum from n=1 to infinity of 1/(n+e^n)	\sum\:_{n=1}^{\infty\:}\frac{1}{n+e^{n}}
sum from n=0 to infinity of (1)^n	\sum\:_{n=0}^{\infty\:}(1)^{n}
f(x)=3x^2-4	f(x)=3x^{2}-4
(\partial)/(\partial y)(yzln(xy))	\frac{\partial\:}{\partial\:y}(yz\ln(xy))
(\partial)/(\partial x)(sin(pi(5x-6y)))	\frac{\partial\:}{\partial\:x}(\sin(π(5x-6y)))
lcm x, 1/(x+y)	lcm\:x,\frac{1}{x+y}
(2+x)y^'=3y	(2+x)y^{\prime\:}=3y
(\partial)/(\partial x)(20sqrt(xy))	\frac{\partial\:}{\partial\:x}(20\sqrt{xy})
integral from 0 to 2 of 1/(sqrt(4+t^2))	\int\:_{0}^{2}\frac{1}{\sqrt{4+t^{2}}}dt
slope of (34)(3-4)	slope\:(34)(3-4)
derivative of x^2+xy+y^3	\frac{d}{dx}(x^{2}+xy+y^{3})
derivative of sqrt(cos(x))	derivative\:\sqrt{\cos(x)}
integral from 1 to 3 of x+2	\int\:_{1}^{3}x+2dx
3y^'+12y=4	3y^{\prime\:}+12y=4
integral of (2arcsin(x))/(sqrt(1-x^2))	\int\:\frac{2\arcsin(x)}{\sqrt{1-x^{2}}}dx
derivative of 2x^2-2x+C	derivative\:2x^{2}-2x+C
integral of 5/(x^7)	\int\:\frac{5}{x^{7}}dx
derivative of 4e^{-x^2}x^3-6e^{-x^2}x	\frac{d}{dx}(4e^{-x^{2}}x^{3}-6e^{-x^{2}}x)
y^{''}+36y=36sin(6x)	y^{\prime\:\prime\:}+36y=36\sin(6x)
integral of (sqrt(324-x^2))/x	\int\:\frac{\sqrt{324-x^{2}}}{x}dx
(\partial)/(\partial x)(-sqrt(2x))	\frac{\partial\:}{\partial\:x}(-\sqrt{2x})
(\partial)/(\partial y)(x^2+xy^3)	\frac{\partial\:}{\partial\:y}(x^{2}+xy^{3})
5(dy)/(dt)+y=20t	5\frac{dy}{dt}+y=20t
integral of e^{5-2x}	\int\:e^{5-2x}dx
derivative of x^2ln(x+x^3)	\frac{d}{dx}(x^{2}\ln(x)+x^{3})
(dy)/(dx)(x)=y	\frac{dy}{dx}(x)=y
(\partial)/(\partial x)((x-a)^2)	\frac{\partial\:}{\partial\:x}((x-a)^{2})
integral of 1/(2x+6)	\int\:\frac{1}{2x+6}dx
integral of cos(pix)	\int\:\cos(pix)dx
(dy)/(dx)+4y=xe^{-4x}	\frac{dy}{dx}+4y=xe^{-4x}
derivative of 4-\|x\|	\frac{d}{dx}(4-\left\|x\right\|)
integral of (e^{3x})/((1-2e^{3x))^2}	\int\:\frac{e^{3x}}{(1-2e^{3x})^{2}}dx
derivative of 1-(1+xe^{-x})	\frac{d}{dx}(1-(1+x)e^{-x})
integral of 1/((2+x)sqrt(1+x))	\int\:\frac{1}{(2+x)\sqrt{1+x}}dx
tangent of f(x)=x^4-2x^2+1,\at x=2	tangent\:f(x)=x^{4}-2x^{2}+1,\at\:x=2
integral from 0 to pi of sin(x)sin(3x)	\int\:_{0}^{π}\sin(x)\sin(3x)dx
derivative of (x^2)/(x^2+3)	derivative\:\frac{x^{2}}{x^{2}+3}
y^'=x^2y-y+x^2-1	y^{\prime\:}=x^{2}y-y+x^{2}-1
integral of e[2x]	\int\:e[2x]dx
integral of (3x)/(sqrt(x^2-1))	\int\:\frac{3x}{\sqrt{x^{2}-1}}dx
integral from 0.1 to 1 of 1.5x^2	\int\:_{0.1}^{1}1.5x^{2}dx
limit as x approaches 4 of x/(-7x+1)	\lim\:_{x\to\:4}(\frac{x}{-7x+1})
(\partial)/(\partial x)(x^2ln(xy))	\frac{\partial\:}{\partial\:x}(x^{2}\ln(xy))
integral from 1 to x of e^{x^2}	\int\:_{1}^{x}e^{x^{2}}dx
derivative of 12x^2-12x	\frac{d}{dx}(12x^{2}-12x)
d/(dj)(4i+5j)	\frac{d}{dj}(4i+5j)
derivative of (e^x)/(3x^2)	derivative\:\frac{e^{x}}{3x^{2}}
derivative of (4x^3+3^2(5x^2+3))	\frac{d}{dx}((4x^{3}+3)^{2}(5x^{2}+3))
integral of (3+u)/u	\int\:\frac{3+u}{u}du
y^{''}+6y^'+34y=0,y(0)=4,y^'(0)=-11	y^{\prime\:\prime\:}+6y^{\prime\:}+34y=0,y(0)=4,y^{\prime\:}(0)=-11
x^3y^'+3x^2y= 1/x	x^{3}y^{\prime\:}+3x^{2}y=\frac{1}{x}
integral of (5/(x^8)-7/(\sqrt[4]{x^3)})	\int\:(\frac{5}{x^{8}}-\frac{7}{\sqrt[4]{x^{3}}})dx
derivative of \sqrt[4]{8x^2}	\frac{d}{dx}(\sqrt[4]{8x^{2}})
derivative of 5x^2sin(x+4x)	\frac{d}{dx}(5x^{2}\sin(x)+4x)
derivative of f(x)=(x^4+c_{1})/(4x^2)	derivative\:f(x)=\frac{x^{4}+c_{1}}{4x^{2}}
integral of sqrt(55-6x-x^2)	\int\:\sqrt{55-6x-x^{2}}dx
limit as n approaches infinity of 28n+4	\lim\:_{n\to\:\infty\:}(28n+4)
derivative of (ax+b)/(cx+d)	derivative\:\frac{ax+b}{cx+d}
integral of x/(x^2+4x+4)	\int\:\frac{x}{x^{2}+4x+4}dx
derivative of 2xe^{2x}+2x^2e^{2x}	\frac{d}{dx}(2xe^{2x}+2x^{2}e^{2x})
integral of asin(x)	\int\:a\sin(x)dx
derivative of cos(x^2+y^2)	\frac{d}{dx}(\cos(x^{2}+y^{2}))
area y^2=4x,y=2x+4	area\:y^{2}=4x,y=2x+4
area y=3-x,y=9-x^2	area\:y=3-x,y=9-x^{2}
limit as x approaches 5+of (\|5-x\|)/(5-x)	\lim\:_{x\to\:5+}(\frac{\left\|5-x\right\|}{5-x})
y^{''}+9y=-30sin(3t)	y^{\prime\:\prime\:}+9y=-30\sin(3t)
derivative of ln(sec(x-tan(x)))	\frac{d}{dx}(\ln(\sec(x)-\tan(x)))
(\partial)/(\partial x)(xe^{(xy)})	\frac{\partial\:}{\partial\:x}(xe^{(xy)})
limit as x approaches 0 of (1+2/x)^x	\lim\:_{x\to\:0}((1+\frac{2}{x})^{x})
derivative of (2-x/x)	\frac{d}{dx}(\frac{2-x}{x})
derivative of ln(5x)	derivative\:\ln(5x)
integral from-pi to pi of cos(nx)	\int\:_{-π}^{π}\cos(nx)dx
y^'=cos(x)	y^{\prime\:}=\cos(x)
inverse oflaplace (e^{-2s})/(s+3)	inverselaplace\:\frac{e^{-2s}}{s+3}
derivative of x^2*tan(x)	\frac{d}{dx}(x^{2}\cdot\:\tan(x))
area x=-2,x=2,y=4x,y=x^2-5	area\:x=-2,x=2,y=4x,y=x^{2}-5
derivative of t^2	derivative\:t^{2}
derivative of 2^{-x^2}	\frac{d}{dx}(2^{-x^{2}})
inverse oflaplace (s+3)/(s^2+6s+13)	inverselaplace\:\frac{s+3}{s^{2}+6s+13}
derivative of x\times log_{10}(x)	\frac{d}{dx}(x\times\:\log_{10}(x))
integral of tan^3(x)sec^{10}(x)	\int\:\tan^{3}(x)\sec^{10}(x)dx
integral of 6x(x^2+1)^{1/2}	\int\:6x(x^{2}+1)^{\frac{1}{2}}dx
integral of (3x-sin(x))	\int\:(3x-\sin(x))dx
(\partial)/(\partial y)(2x^3y-3)	\frac{\partial\:}{\partial\:y}(2x^{3}y-3)
simplify (5X^4-3X^3)/(X^5)	simplify\:\frac{5X^{4}-3X^{3}}{X^{5}}

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