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Popular Calculus Problems

derivative of f(x)=3x(18x^4+(13)/(x+1))	derivative\:f(x)=3x(18x^{4}+\frac{13}{x+1})
derivative of (6x^2+6x+6/(sqrt(x)))	\frac{d}{dx}(\frac{6x^{2}+6x+6}{\sqrt{x}})
area ln(2x), 1/2 ,(e^2)/2	area\:\ln(2x),\frac{1}{2},\frac{e^{2}}{2}
derivative of 3^{2x}	derivative\:3^{2x}
(\partial)/(\partial x)(x^2+y^2-5)	\frac{\partial\:}{\partial\:x}(x^{2}+y^{2}-5)
(dy)/(dx)=sqrt(5y)e^{x+2}	\frac{dy}{dx}=\sqrt{5y}e^{x+2}
f(x)=sqrt(2x^2-7)	f(x)=\sqrt{2x^{2}-7}
integral from 0 to 1 of (2x)/((x^2+1)^2)	\int\:_{0}^{1}\frac{2x}{(x^{2}+1)^{2}}dx
area x= 1/2 y^2,y=1,y=-1/2 x+3	area\:x=\frac{1}{2}y^{2},y=1,y=-\frac{1}{2}x+3
(\partial)/(\partial y)((-y)/(y^2+x^2))	\frac{\partial\:}{\partial\:y}(\frac{-y}{y^{2}+x^{2}})
derivative of (3x-1/(sqrt(x^2+2)))	\frac{d}{dx}(\frac{3x-1}{\sqrt{x^{2}+2}})
derivative of sin(8cos(x))	\frac{d}{dx}(\sin(8\cos(x)))
integral of (tan^3(θ))/(cos^4(θ))	\int\:\frac{\tan^{3}(θ)}{\cos^{4}(θ)}dθ
xy^{''}+y^'=0	xy^{\prime\:\prime\:}+y^{\prime\:}=0
derivative of pi^{sqrt(x)}	\frac{d}{dx}(π^{\sqrt{x}})
(\partial}{\partial x}(\frac{sin(x))/x)	\frac{\partial\:}{\partial\:x}(\frac{\sin(x)}{x})
y^{''}-2y^'+10y=0,y(0)=4,y^'(0)=1	y^{\prime\:\prime\:}-2y^{\prime\:}+10y=0,y(0)=4,y^{\prime\:}(0)=1
limit as x approaches-9-of x^2+3/(x+9)	\lim\:_{x\to\:-9-}(x^{2}+\frac{3}{x+9})
(\partial)/(\partial y)((-y)/(2x^2+y^2))	\frac{\partial\:}{\partial\:y}(\frac{-y}{2x^{2}+y^{2}})
integral of (3z+z^2)sin(z)	\int\:(3z+z^{2})\sin(z)dz
derivative of (x-sqrt(x))/(x^{1/5)}	derivative\:\frac{x-\sqrt{x}}{x^{\frac{1}{5}}}
integral of (in(x))/(x^2)	\int\:\frac{in(x)}{x^{2}}dx
derivative of (3x/(4x-2))	\frac{d}{dx}(\frac{3x}{4x-2})
y^'+(7y)/(x+3)=(x+3)^3	y^{\prime\:}+\frac{7y}{x+3}=(x+3)^{3}
integral of t/((t^2+1)^{3/2)}	\int\:\frac{t}{(t^{2}+1)^{\frac{3}{2}}}dt
integral of (13x)/(x+3)	\int\:\frac{13x}{x+3}dx
limit as x approaches 2 of (5x-3)/4	\lim\:_{x\to\:2}(\frac{5x-3}{4})
integral of sqrt(25x^2-4)	\int\:\sqrt{25x^{2}-4}dx
integral of cos(θ)sin^8(θ)	\int\:\cos(θ)\sin^{8}(θ)dθ
integral of sqrt(2x)	\int\:\sqrt{2x}dx
integral of (e^x)/(e^{2x)+2e^x+1}	\int\:\frac{e^{x}}{e^{2x}+2e^{x}+1}dx
integral of 3/(y^3)	\int\:\frac{3}{y^{3}}dy
tangent of f(x)=x^2-4,\at 5	tangent\:f(x)=x^{2}-4,\at\:5
integral of xsin(x)	\int\:x\sin(x)dx
derivative of ln(1)	derivative\:\ln(1)
limit as x approaches infinity of 11/2	\lim\:_{x\to\:\infty\:}(\frac{11}{2})
integral from 2 to 5 of 1/(x^2-1)	\int\:_{2}^{5}\frac{1}{x^{2}-1}dx
(\partial)/(\partial z)(e^{2z}x+2z)	\frac{\partial\:}{\partial\:z}(e^{2z}x+2z)
(\partial)/(\partial x)(xyln(x^2+2y^2))	\frac{\partial\:}{\partial\:x}(xy\ln(x^{2}+2y^{2}))
limit as x approaches+0-of e^{7/x}	\lim\:_{x\to\:+0-}(e^{\frac{7}{x}})
derivative of \sqrt[3]{x}+1/(x^2)	derivative\:\sqrt[3]{x}+\frac{1}{x^{2}}
(\partial)/(\partial x)(-1/((10+x*y)))	\frac{\partial\:}{\partial\:x}(-\frac{1}{(10+x\cdot\:y)})
derivative of x(8^{-2x})	derivative\:x(8^{-2x})
laplacetransform 3/2 sin(2t)	laplacetransform\:\frac{3}{2}\sin(2t)
limit as x approaches 3 of 1/(x-3)	\lim\:_{x\to\:3}(\frac{1}{x-3})
f(x)=cos^2(2-x^2)	f(x)=\cos^{2}(2-x^{2})
integral of 1/(a^2+b^2x^2)	\int\:\frac{1}{a^{2}+b^{2}x^{2}}dx
integral from 0 to 8 of 1/(sqrt(1+x))	\int\:_{0}^{8}\frac{1}{\sqrt{1+x}}dx
integral of 2xy-9x^2	\int\:2xy-9x^{2}dx
integral from 2 to 4 of 10+4x-3x^3	\int\:_{2}^{4}10+4x-3x^{3}dx
tangent of 2x-2x^2	tangent\:2x-2x^{2}
derivative of 0.9x^33^x	derivative\:0.9x^{3}3^{x}
(\partial)/(\partial x)((4sqrt(x))/(3y^2+1))	\frac{\partial\:}{\partial\:x}(\frac{4\sqrt{x}}{3y^{2}+1})
derivative of 3x^2-1-x^3	\frac{d}{dx}(3x^{2}-1-x^{3})
integral of e^{11x}(11)	\int\:e^{11x}(11)dx
integral of x^3tan(xy)	\int\:x^{3}\tan(xy)dy
derivative of-x^2+1	\frac{d}{dx}(-x^{2}+1)
-y+x(dy)/(dx)ln(x)=0	-y+x\frac{dy}{dx}\ln(x)=0
integral of cos(wt)e^{-st}	\int\:\cos(wt)e^{-st}dt
integral of xln(x^4)	\int\:x\ln(x^{4})dx
derivative of (x-1^2(x+3))	\frac{d}{dx}((x-1)^{2}(x+3))
derivative of mx+b	derivative\:mx+b
(\partial)/(\partial x)(-ksqrt(p(x)gx+A))	\frac{\partial\:}{\partial\:x}(-k\sqrt{p(x)gx+A})
integral from 0 to 2 of a^{x/2}	\int\:_{0}^{2}a^{\frac{x}{2}}dx
integral of-9/x	\int\:-\frac{9}{x}dx
integral from 1 to 5 of (x^2+7)/(6x-x^2)	\int\:_{1}^{5}\frac{x^{2}+7}{6x-x^{2}}dx
limit as n approaches infinity of 7n	\lim\:_{n\to\:\infty\:}(7n)
integral of 0.5	\int\:0.5
integral of x^5tan^3(x^6)	\int\:x^{5}\tan^{3}(x^{6})dx
integral from-1 to 27 of 1/(\sqrt[3]{x)}	\int\:_{-1}^{27}\frac{1}{\sqrt[3]{x}}dx
integral of (e^{9/t})/(t^2)	\int\:\frac{e^{\frac{9}{t}}}{t^{2}}dt
derivative of (x^3/(3!))	\frac{d}{dx}(\frac{x^{3}}{3!})
integral of (6x+5)^2	\int\:(6x+5)^{2}dx
derivative of b	derivative\:b
2y(x^2-y+x)dx+(x^2-2y)dy=0	2y(x^{2}-y+x)dx+(x^{2}-2y)dy=0
integral from 0 to 4 of 2	\int\:_{0}^{4}2dx
derivative of tan(3x-1)	\frac{d}{dx}(\tan(3x-1))
integral of-2x^2e^{8(x^2)}-2xe^{-8x}	\int\:-2x^{2}e^{8(x^{2})}-2xe^{-8x}dx
derivative of arcsin(-4x)	\frac{d}{dx}(\arcsin(-4x))
sum from n=0 to infinity of 2/(3^{n+1)}	\sum\:_{n=0}^{\infty\:}\frac{2}{3^{n+1}}
y^{''}-b^2y=0	y^{\prime\:\prime\:}-b^{2}y=0
integral of (ln(2)x^5)/(x^2)	\int\:\frac{\ln(2)x^{5}}{x^{2}}dx
integral from 0 to 4 of sqrt(x)-(x-2)	\int\:_{0}^{4}\sqrt{x}-(x-2)dx
x^{''}+x=0,x(pi/2)=0,x^'(pi/2)=1	x^{\prime\:\prime\:}+x=0,x(\frac{π}{2})=0,x^{\prime\:}(\frac{π}{2})=1
integral of a^xx	\int\:a^{x}xdx
area y=2x^2,y=8x-2x^2	area\:y=2x^{2},y=8x-2x^{2}
(\partial)/(\partial y)(x^2+y^2-13)	\frac{\partial\:}{\partial\:y}(x^{2}+y^{2}-13)
tangent of f(x)=-x^2-7x+44,\at x=2	tangent\:f(x)=-x^{2}-7x+44,\at\:x=2
integral of-e^{3x}	\int\:-e^{3x}dx
derivative of (2(-x^2+1))/((x^2+1)^2)	derivative\:\frac{2(-x^{2}+1)}{(x^{2}+1)^{2}}
integral of y/(xz)	\int\:\frac{y}{xz}dx
inverse oflaplace (s+2)/((s-2)(s+1))	inverselaplace\:\frac{s+2}{(s-2)(s+1)}
integral of 2xy-sin(x)	\int\:2xy-\sin(x)dx
derivative of f(x)=(x+1)(3x^2-5x+2)	derivative\:f(x)=(x+1)(3x^{2}-5x+2)
y^{''}-y^'-y=0	y^{\prime\:\prime\:}-y^{\prime\:}-y=0
limit as x approaches 4 of 2x-1	\lim\:_{x\to\:4}(2x-1)
derivative of 2e^xln(x)	\frac{d}{dx}(2e^{x}\ln(x))
limit as x approaches-2 of-x^2+8x-4	\lim\:_{x\to\:-2}(-x^{2}+8x-4)
integral of (28)/((1-x^2)^{3/2)}	\int\:\frac{28}{(1-x^{2})^{\frac{3}{2}}}dx
(1x+ye^{y/x})dx-xe^{y/x}dy=0,y(1)=3	(1x+ye^{\frac{y}{x}})dx-xe^{\frac{y}{x}}dy=0,y(1)=3

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