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Popular Calculus Problems

(d^4)/(dx^4)((10x)/(1-x))	\frac{d^{4}}{dx^{4}}(\frac{10x}{1-x})
derivative of f(x)=e^{5x^2}	derivative\:f(x)=e^{5x^{2}}
tangent of y=sin(2x),\at x= pi/2	tangent\:y=\sin(2x),\at\:x=\frac{π}{2}
tangent of 2x^2+3x-2,\at x=0	tangent\:2x^{2}+3x-2,\at\:x=0
derivative of f(x)= 3/(x^2)+5/(x^4)	derivative\:f(x)=\frac{3}{x^{2}}+\frac{5}{x^{4}}
(dy)/(dx)=4x+(4x)/(sqrt(16-x^2))	\frac{dy}{dx}=4x+\frac{4x}{\sqrt{16-x^{2}}}
limit as x approaches 8 of (3x^2)/4	\lim\:_{x\to\:8}(\frac{3x^{2}}{4})
integral of (xe^{2x})/((1+2x)^2)	\int\:\frac{xe^{2x}}{(1+2x)^{2}}dx
y^{''}+4y^'+3y=65sin(2t)	y^{\prime\:\prime\:}+4y^{\prime\:}+3y=65\sin(2t)
derivative of f(x)=3-x	derivative\:f(x)=3-x
area x^2+1,x,[0,1]	area\:x^{2}+1,x,[0,1]
(\partial)/(\partial x)(3xy^2-2y+5x^2y^2)	\frac{\partial\:}{\partial\:x}(3xy^{2}-2y+5x^{2}y^{2})
tangent of f(x)=sqrt(x+3),\at x=-2	tangent\:f(x)=\sqrt{x+3},\at\:x=-2
derivative of s^2	derivative\:s^{2}
derivative of nlog_{2}(n)	derivative\:n\log_{2}(n)
integral of 1/(sin(u)+1)	\int\:\frac{1}{\sin(u)+1}du
y^'=(x^2y^4+3x^2)/(y^3)	y^{\prime\:}=\frac{x^{2}y^{4}+3x^{2}}{y^{3}}
sum from n=1 to infinity of 1/n (3/2)^n	\sum\:_{n=1}^{\infty\:}\frac{1}{n}(\frac{3}{2})^{n}
limit as x approaches 4 of (7x-1)/(x-4)	\lim\:_{x\to\:4}(\frac{7x-1}{x-4})
derivative of 3e^{4x^2}	\frac{d}{dx}(3e^{4x^{2}})
inverse oflaplace s/((s^2+9)*(s^2+16))	inverselaplace\:\frac{s}{(s^{2}+9)\cdot\:(s^{2}+16)}
maclaurin ln((1+x)/(1-x))	maclaurin\:\ln(\frac{1+x}{1-x})
(\partial)/(\partial y)(4x^3y^3-2)	\frac{\partial\:}{\partial\:y}(4x^{3}y^{3}-2)
derivative of f(x)=(4+cot(x))/(7-tan(x))	derivative\:f(x)=\frac{4+\cot(x)}{7-\tan(x)}
derivative of 5t	derivative\:5t
inverse oflaplace 6/(s(s+1)(s+2)+6)	inverselaplace\:\frac{6}{s(s+1)(s+2)+6}
integral of sin(3)x^2	\int\:\sin(3)x^{2}dx
derivative of (x^2/(a^2))	\frac{d}{dx}(\frac{x^{2}}{a^{2}})
limit as x approaches infinity of sqrt(x)	\lim\:_{x\to\:\infty\:}(\sqrt{x})
limit as x approaches 0 of tan^2(x)	\lim\:_{x\to\:0}(\tan^{2}(x))
integral of (e^x+1)(x-4)	\int\:(e^{x}+1)(x-4)dx
limit as x approaches 1+of (x)^{1/(x-1)}	\lim\:_{x\to\:1+}((x)^{\frac{1}{x-1}})
area (x-1)^2+2,(-1,2)	area\:(x-1)^{2}+2,(-1,2)
(\partial)/(\partial x)(-y/(y^2+x^2))	\frac{\partial\:}{\partial\:x}(-\frac{y}{y^{2}+x^{2}})
tangent of x/(sqrt(4+x^2))	tangent\:\frac{x}{\sqrt{4+x^{2}}}
y^'+y=xy^3	y^{\prime\:}+y=xy^{3}
derivative of y=((x^2+3)/(x^2-3))^4	derivative\:y=(\frac{x^{2}+3}{x^{2}-3})^{4}
limit as x approaches 1 of sqrt(-x)	\lim\:_{x\to\:1}(\sqrt{-x})
((1+x)dy)/(dx)-xy=x+x^2	\frac{(1+x)dy}{dx}-xy=x+x^{2}
derivative of (e^{7x})/(ln(6x))	derivative\:\frac{e^{7x}}{\ln(6x)}
derivative of 3x^2-4x+3	\frac{d}{dx}(3x^{2}-4x+3)
derivative of 1/(6+x^2)	\frac{d}{dx}(\frac{1}{6+x^{2}})
derivative of y=(e^x)/x	derivative\:y=\frac{e^{x}}{x}
tangent of f(x)=x^4-17x^2+16,\at x=2	tangent\:f(x)=x^{4}-17x^{2}+16,\at\:x=2
area-x^2+10,-sqrt(10),-1	area\:-x^{2}+10,-\sqrt{10},-1
integral of 1/(sin^2(x)*cos^2(x))	\int\:\frac{1}{\sin^{2}(x)\cdot\:\cos^{2}(x)}dx
y^{''}+6y^'+9y=(e^{-3x})/x	y^{\prime\:\prime\:}+6y^{\prime\:}+9y=\frac{e^{-3x}}{x}
integral of (sqrt(2x)+1)^3\sqrt[4]{5/x}	\int\:(\sqrt{2x}+1)^{3}\sqrt[4]{\frac{5}{x}}dx
sum from n=1 to infinity of 0	\sum\:_{n=1}^{\infty\:}0
sum from n=1 to infinity of (e/(10))^n	\sum\:_{n=1}^{\infty\:}(\frac{e}{10})^{n}
laplacetransform 7t+3	laplacetransform\:7t+3
integral from 3 to 8 of sqrt(1+x)	\int\:_{3}^{8}\sqrt{1+x}dx
integral of 7sin(sqrt(x))	\int\:7\sin(\sqrt{x})dx
derivative of (5x)/(sqrt(3x-2))	derivative\:\frac{5x}{\sqrt{3x-2}}
integral of (2x^4)/(x^2-2x)	\int\:\frac{2x^{4}}{x^{2}-2x}dx
integral from 0 to 1 of xsqrt(1+4x^2)	\int\:_{0}^{1}x\sqrt{1+4x^{2}}dx
(\partial)/(\partial x)(x^2-5xy)	\frac{\partial\:}{\partial\:x}(x^{2}-5xy)
derivative of f(x)=x^{1.7}	derivative\:f(x)=x^{1.7}
limit as x approaches-4 of (x^2+9)/(x+2)	\lim\:_{x\to\:-4}(\frac{x^{2}+9}{x+2})
integral of 16e^u	\int\:16e^{u}du
y^{''}-4y^'-x+2=0	y^{\prime\:\prime\:}-4y^{\prime\:}-x+2=0
derivative of \|x^3+2x^2-4x-8\|	\frac{d}{dx}(\left\|x^{3}+2x^{2}-4x-8\right\|)
limit as x approaches 4 of 3e^{1.7x}+1	\lim\:_{x\to\:4}(3e^{1.7x}+1)
y^{''}-4y^'+4y=8x^2+e^{2x}	y^{\prime\:\prime\:}-4y^{\prime\:}+4y=8x^{2}+e^{2x}
derivative of y=3x^3+45x^2+81x	derivative\:y=3x^{3}+45x^{2}+81x
integral of 1/(xsqrt(x+4))	\int\:\frac{1}{x\sqrt{x+4}}dx
area y=sin^2(x),y=sin^3(x)	area\:y=\sin^{2}(x),y=\sin^{3}(x)
integral of 4/(4x^2+20x+34)	\int\:\frac{4}{4x^{2}+20x+34}dx
integral from 0 to r of-pir^2x	\int\:_{0}^{r}-πr^{2}xdx
integral of 8x^7e^{2x^8}	\int\:8x^{7}e^{2x^{8}}dx
derivative of arccos(ax)	derivative\:\arccos(ax)
(\partial)/(\partial x)(x^2+y^2+10)	\frac{\partial\:}{\partial\:x}(x^{2}+y^{2}+10)
integral from 0 to infinity of 15e^{-5x}	\int\:_{0}^{\infty\:}15e^{-5x}dx
tangent of f(x)=6x-x^2,(1,5)	tangent\:f(x)=6x-x^{2},(1,5)
derivative of f(x)= 1/(sqrt(x+8))	derivative\:f(x)=\frac{1}{\sqrt{x+8}}
y^'-y=xe^{2x}+1	y^{\prime\:}-y=xe^{2x}+1
derivative of 5^{2x^3}	\frac{d}{dx}(5^{2x^{3}})
xy^'=4x^2-2y,y(1)=3	xy^{\prime\:}=4x^{2}-2y,y(1)=3
area y^2-27x=0,x+y=0	area\:y^{2}-27x=0,x+y=0
tangent of f(x)=x^3+4x-2,\at x=1	tangent\:f(x)=x^{3}+4x-2,\at\:x=1
derivative of (x^{n+1}/(n+1))	\frac{d}{dx}(\frac{x^{n+1}}{n+1})
derivative of 50ln(2x+1)-x/2	derivative\:50\ln(2x+1)-\frac{x}{2}
integral from 5 to infinity of 2/(x^3)	\int\:_{5}^{\infty\:}\frac{2}{x^{3}}dx
inverse oflaplace (5s+2)/((s+1)(s+2)^2)	inverselaplace\:\frac{5s+2}{(s+1)(s+2)^{2}}
integral of-10x^{2/3}	\int\:-10x^{\frac{2}{3}}dx
integral of (x-6)^2	\int\:(x-6)^{2}dx
area 2x^2,4-2x,-2,2	area\:2x^{2},4-2x,-2,2
integral from 0 to 1 of cos(pit)	\int\:_{0}^{1}\cos(πt)dt
derivative of cos(x^2+5)-x^3	derivative\:\cos(x^{2}+5)-x^{3}
derivative of ln((5+e^x/(5-e^x)))	\frac{d}{dx}(\ln(\frac{5+e^{x}}{5-e^{x}}))
limit as x approaches infinity of (arctan(x))/(1/x-4)	\lim\:_{x\to\:\infty\:}(\frac{\arctan(x)}{\frac{1}{x}-4})
derivative of-(x^7/7+(x^5)/5)	\frac{d}{dx}(-\frac{x^{7}}{7}+\frac{x^{5}}{5})
derivative of y=(3x-2)/(2x+1)	derivative\:y=\frac{3x-2}{2x+1}
(\partial)/(\partial x)((2y)/((x+y)^2))	\frac{\partial\:}{\partial\:x}(\frac{2y}{(x+y)^{2}})
integral of (x^3)/((x^2+a^2)^3)	\int\:\frac{x^{3}}{(x^{2}+a^{2})^{3}}dx
area y=3sqrt(x),x+y=4,y=1	area\:y=3\sqrt{x},x+y=4,y=1
integral from-1 to 1 of (5r)/((4+r^2)^2)	\int\:_{-1}^{1}\frac{5r}{(4+r^{2})^{2}}dr
(\partial)/(\partial x)(x/(x^2+xy+y^2))	\frac{\partial\:}{\partial\:x}(\frac{x}{x^{2}+xy+y^{2}})
integral of (3x-2)/(5x^2-3x+2)	\int\:\frac{3x-2}{5x^{2}-3x+2}dx
derivative of 55cos(0.03x-1.11)+86	derivative\:55\cos(0.03x-1.11)+86

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