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Popular Calculus Problems

x^2y^'+2xy=7cos^2(x)	x^{2}y^{\prime\:}+2xy=7\cos^{2}(x)
integral of ((sin(2x))/(cos(x)))	\int\:(\frac{\sin(2x)}{\cos(x)})dx
derivative of (x^6/5)	\frac{d}{dx}(\frac{x^{6}}{5})
derivative of y/(x+y)	\frac{d}{dx}(\frac{y}{x+y})
derivative of f(x)=-1/7 (x^{-7}-x^{14})	derivative\:f(x)=-\frac{1}{7}(x^{-7}-x^{14})
derivative of sqrt(x)csc(x)	derivative\:\sqrt{x}\csc(x)
xxy^'=y^2+1	xxy^{\prime\:}=y^{2}+1
5y^{''}+25y^'+1700y=0	5y^{\prime\:\prime\:}+25y^{\prime\:}+1700y=0
derivative of y=arccos(3x)	derivative\:y=\arccos(3x)
slope of (-5,-5),(5,5)	slope\:(-5,-5),(5,5)
integral of 1/(x^2)sqrt(7+1/x)	\int\:\frac{1}{x^{2}}\sqrt{7+\frac{1}{x}}dx
derivative of x^4-5x	\frac{d}{dx}(x^{4}-5x)
derivative of 2cos(x)-2sin(x)	derivative\:2\cos(x)-2\sin(x)
integral from 0 to 1 of 8/(sqrt(1-x^2))	\int\:_{0}^{1}\frac{8}{\sqrt{1-x^{2}}}dx
integral of 2tcos(t)	\int\:2t\cos(t)dt
derivative of 3sqrt(x)-(11/(x^{12)})	\frac{d}{dx}(3\sqrt{x}-\frac{11}{x^{12}})
tangent of f(x)=7x-6sqrt(x),(1,1)	tangent\:f(x)=7x-6\sqrt{x},(1,1)
y^{'''}-y^{''}+y^'-y=x	y^{\prime\:\prime\:\prime\:}-y^{\prime\:\prime\:}+y^{\prime\:}-y=x
(\partial)/(\partial x)(e^x*sin(x))	\frac{\partial\:}{\partial\:x}(e^{x}\cdot\:\sin(x))
8y^'=3e^{x/8}+y	8y^{\prime\:}=3e^{\frac{x}{8}}+y
derivative of (8x/(3-cot(x)))	\frac{d}{dx}(\frac{8x}{3-\cot(x)})
integral of 1/(e^{2x)-2e^x}	\int\:\frac{1}{e^{2x}-2e^{x}}dx
integral of e^{-θ}cos(5θ)	\int\:e^{-θ}\cos(5θ)dθ
xy^'-y=-x^2-2x+2	xy^{\prime\:}-y=-x^{2}-2x+2
integral of (sqrt(2t)-cos(6t))	\int\:(\sqrt{2t}-\cos(6t))dt
derivative of (2x-3)^4	derivative\:(2x-3)^{4}
integral of (1/3)/(x^2-x+1)	\int\:\frac{\frac{1}{3}}{x^{2}-x+1}dx
derivative of 8sqrt(x)	derivative\:8\sqrt{x}
integral of (3x)/(1-4x^2)	\int\:\frac{3x}{1-4x^{2}}dx
integral of 1+sqrt(9-x^2)	\int\:1+\sqrt{9-x^{2}}dx
derivative of f(x)=x^3-3x^2-9x+2	derivative\:f(x)=x^{3}-3x^{2}-9x+2
integral from 1 to b of 1/(x^2)	\int\:_{1}^{b}\frac{1}{x^{2}}dx
integral of sin(sqrt(x+4))	\int\:\sin(\sqrt{x+4})dx
y^'+cos(x)y=2cos(x)	y^{\prime\:}+\cos(x)y=2\cos(x)
limit as x approaches-1-of x	\lim\:_{x\to\:-1-}(x)
derivative of f(x)=5arcsin(x^4)	derivative\:f(x)=5\arcsin(x^{4})
derivative of sqrt(1-25x^2)arccos(5x)	\frac{d}{dx}(\sqrt{1-25x^{2}}\arccos(5x))
x^'=2(x+1),x(0)=0	x^{\prime\:}=2(x+1),x(0)=0
integral of cos((xy)/2)	\int\:\cos(\frac{xy}{2})dy
derivative of 1-(x-3^{2/3})	\frac{d}{dx}(1-(x-3)^{\frac{2}{3}})
integral of e^{-0.01x}	\int\:e^{-0.01x}dx
derivative of 10sin^2(x)+10cos^2(x)	derivative\:10\sin^{2}(x)+10\cos^{2}(x)
taylor e^{-4x}	taylor\:e^{-4x}
derivative of (8x/(8+sqrt(x)))	\frac{d}{dx}(\frac{8x}{8+\sqrt{x}})
1/(2x)y^'= x/(3y)	\frac{1}{2x}y^{\prime\:}=\frac{x}{3y}
(dy)/(dx)=(sqrt(y^2-9))	\frac{dy}{dx}=(\sqrt{y^{2}-9})
(\partial)/(\partial x)(e^{-5t}cos(pix))	\frac{\partial\:}{\partial\:x}(e^{-5t}\cos(πx))
limit as x approaches-1 of-1	\lim\:_{x\to\:-1}(-1)
integral of 2x(x^2+13)^7	\int\:2x(x^{2}+13)^{7}dx
slope of (6,1),(4,3)	slope\:(6,1),(4,3)
derivative of f(x)=x^2cos^2(x\at x)=-2	derivative\:f(x)=x^{2}\cos^{2}(x\at\:x)=-2
derivative of 5x^2-3	derivative\:5x^{2}-3
(d^2)/(dx^2)(xe^{1/x})	\frac{d^{2}}{dx^{2}}(xe^{\frac{1}{x}})
integral from-1 to 0 of 20(e^{1/x})/(x^3)	\int\:_{-1}^{0}20\frac{e^{\frac{1}{x}}}{x^{3}}dx
(sqrt(x-1))^'	(\sqrt{x-1})^{\prime\:}
derivative of ((ax+b)/((cx+d)))	\frac{d}{dx}(\frac{(ax+b)}{(cx+d)})
integral of 7/(3+7x^2)	\int\:\frac{7}{3+7x^{2}}dx
sum from n=2 to infinity of ne^{-n}	\sum\:_{n=2}^{\infty\:}ne^{-n}
derivative of f(x)=e^{4a}(4a^3-3)	derivative\:f(x)=e^{4a}(4a^{3}-3)
derivative of ln(sqrt(tan(x)))	\frac{d}{dx}(\ln(\sqrt{\tan(x)}))
integral of 7x^2sqrt(x^3+15)	\int\:7x^{2}\sqrt{x^{3}+15}dx
(dy)/(dx)=3x+y	\frac{dy}{dx}=3x+y
tangent of 9x-9x	tangent\:9x-9x
derivative of ln((a^x/(1+a^x)))	\frac{d}{dx}(\ln(\frac{a^{x}}{1+a^{x}}))
(1+x)(dy)/(dx)-xy=x-x^2	(1+x)\frac{dy}{dx}-xy=x-x^{2}
(\partial)/(\partial x)(10arccot(x))	\frac{\partial\:}{\partial\:x}(10\arccot(x))
(\partial)/(\partial x)(3x-x^2y^2+2x^3y)	\frac{\partial\:}{\partial\:x}(3x-x^{2}y^{2}+2x^{3}y)
derivative of 2x^{-1/3}	\frac{d}{dx}(2x^{-\frac{1}{3}})
integral of sqrt(24+12x+3x^2)	\int\:\sqrt{24+12x+3x^{2}}dx
derivative of 5/(2x)	derivative\:\frac{5}{2x}
(\partial)/(\partial x)(1/(sqrt(4pit))e^{-(x^2)/(4t)})	\frac{\partial\:}{\partial\:x}(\frac{1}{\sqrt{4πt}}e^{-\frac{x^{2}}{4t}})
(\partial)/(\partial x)((xy)/(5x+3y))	\frac{\partial\:}{\partial\:x}(\frac{xy}{5x+3y})
y(x+9)+y^'=0	y(x+9)+y^{\prime\:}=0
(\partial)/(\partial y)(y^2cos(xy^2))	\frac{\partial\:}{\partial\:y}(y^{2}\cos(xy^{2}))
f(x)=x^3ln(x)	f(x)=x^{3}\ln(x)
integral of (sin(x)y)	\int\:(\sin(x)y)dy
derivative of 5e^{-3x}	\frac{d}{dx}(5e^{-3x})
integral of 1/(4e^{-5x)+e^{5x}}	\int\:\frac{1}{4e^{-5x}+e^{5x}}dx
integral of x/(y^2)	\int\:\frac{x}{y^{2}}dy
inverse oflaplace s/((s+3)^2)	inverselaplace\:\frac{s}{(s+3)^{2}}
x(dy)/(dx)+y=y^2ln(x)	x\frac{dy}{dx}+y=y^{2}\ln(x)
derivative of (87x^3)/(25)	derivative\:\frac{87x^{3}}{25}
tangent of y=(x^3-25x)^{14},(5,0)	tangent\:y=(x^{3}-25x)^{14},(5,0)
integral of θarcsec(4θ)	\int\:θ\arcsec(4θ)dθ
y^'+10y=2cos(t)	y^{\prime\:}+10y=2\cos(t)
xy^'=2y+x^3e^x	xy^{\prime\:}=2y+x^{3}e^{x}
limit as t approaches 1 of 3t^3+2	\lim\:_{t\to\:1}(3t^{3}+2)
integral of x/(1+sqrt(x))	\int\:\frac{x}{1+\sqrt{x}}dx
(\partial)/(\partial x)(-2x)	\frac{\partial\:}{\partial\:x}(-2x)
(\partial)/(\partial x)(xe^{-2x^2-2y^2})	\frac{\partial\:}{\partial\:x}(xe^{-2x^{2}-2y^{2}})
integral of sqrt(2x^2+1)	\int\:\sqrt{2x^{2}+1}dx
derivative of (3x^2+3x-2)/(2xsqrt(x))	derivative\:\frac{3x^{2}+3x-2}{2x\sqrt{x}}
slope ofintercept (5.5)(2.3)	slopeintercept\:(5.5)(2.3)
integral of t^2e^{-5t}	\int\:t^{2}e^{-5t}dt
x^2y^{''}-9xy^'+25y=0	x^{2}y^{\prime\:\prime\:}-9xy^{\prime\:}+25y=0
derivative of f(x)=36x^{-2}-2x^{-4}+2	derivative\:f(x)=36x^{-2}-2x^{-4}+2
derivative of (x+b^2)	\frac{d}{dx}((x+b)^{2})
derivative of a^7+cos^7(x)	derivative\:a^{7}+\cos^{7}(x)
integral from 3 to 4 of (x^3-pix^2)	\int\:_{3}^{4}(x^{3}-πx^{2})dx
derivative of (-7x/(sqrt(2x-1)))	\frac{d}{dx}(\frac{-7x}{\sqrt{2x-1}})

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