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Popular Calculus Problems

derivative of (3x^2-13^3)	\frac{d}{dx}((3x^{2}-13)^{3})
derivative of (sin(x)/(y^2))	\frac{d}{dx}(\frac{\sin(x)}{y^{2}})
derivative of 3*ln(x)	\frac{d}{dx}(3\cdot\:\ln(x))
derivative of-7sqrt(x)	\frac{d}{dx}(-7\sqrt{x})
laplacetransform (1+e^{2t})^2	laplacetransform\:(1+e^{2t})^{2}
2y^{''}+12y^'+50y=0	2y^{\prime\:\prime\:}+12y^{\prime\:}+50y=0
integral of cos^2(2x)sin(2x)	\int\:\cos^{2}(2x)\sin(2x)dx
derivative of 3e^x+x	derivative\:3e^{x}+x
integral of e^xcos(2e^x)	\int\:e^{x}\cos(2e^{x})dx
integral of 5tsin^2(t)	\int\:5t\sin^{2}(t)dt
integral of 12x^2+6x-5	\int\:12x^{2}+6x-5dx
integral from 0 to pi/4 of tan^8(θ)sec^2(θ)	\int\:_{0}^{\frac{π}{4}}\tan^{8}(θ)\sec^{2}(θ)dθ
derivative of (e^x)/(ln(x))	derivative\:\frac{e^{x}}{\ln(x)}
derivative of xt	\frac{d}{dx}(xt)
limit as x approaches-2-of 1/(x-2)	\lim\:_{x\to\:-2-}(\frac{1}{x-2})
derivative of (3x^4-4(3-2x^3))	\frac{d}{dx}((3x^{4}-4)(3-2x^{3}))
derivative of y=xcos(x)sin(x)	derivative\:y=x\cos(x)\sin(x)
(\partial)/(\partial y)(4y(1/x-ln(x)))	\frac{\partial\:}{\partial\:y}(4y(\frac{1}{x}-\ln(x)))
integral from 0 to 9 of 1/(sqrt(x))	\int\:_{0}^{9}\frac{1}{\sqrt{x}}dx
derivative of y=sec(x)tan(x)	derivative\:y=\sec(x)\tan(x)
integral of 7e^{3x}	\int\:7e^{3x}dx
(\partial)/(\partial y)(2/(2x+3y))	\frac{\partial\:}{\partial\:y}(\frac{2}{2x+3y})
derivative of f(x)=x^2sin(x)	derivative\:f(x)=x^{2}\sin(x)
derivative of-x^3+9x^2-6x+9	\frac{d}{dx}(-x^{3}+9x^{2}-6x+9)
derivative of 8/(sqrt(64+64t^2))	derivative\:\frac{8}{\sqrt{64+64t^{2}}}
(dy)/(dx)=2cos(x)(y+1),y(pi/6)=2	\frac{dy}{dx}=2\cos(x)(y+1),y(\frac{π}{6})=2
(\partial)/(\partial x)(2x^2y^2)	\frac{\partial\:}{\partial\:x}(2x^{2}y^{2})
sum from n=0 to infinity of 9(3/4)^n	\sum\:_{n=0}^{\infty\:}9(\frac{3}{4})^{n}
integral of-2y	\int\:-2ydy
derivative of 1/(2y^{3/2)}	derivative\:\frac{1}{2y^{\frac{3}{2}}}
integral from 0 to 1 of 1/(4x-1)	\int\:_{0}^{1}\frac{1}{4x-1}dx
limit as x approaches-1 of arctan((x-1)/(x+1))	\lim\:_{x\to\:-1}(\arctan(\frac{x-1}{x+1}))
derivative of 6x^3	derivative\:6x^{3}
derivative of (5-7x)^3	derivative\:(5-7x)^{3}
(dy)/(dx)=-4y	\frac{dy}{dx}=-4y
integral of 1/(sqrt(9e^{-2x)-1)}	\int\:\frac{1}{\sqrt{9e^{-2x}-1}}dx
y'=y^2-2y	y\prime\:=y^{2}-2y
integral of (5x+3)^3	\int\:(5x+3)^{3}dx
slope ofintercept (-2,-8),(3,2)	slopeintercept\:(-2,-8),(3,2)
slope of (5.5)(4.2)	slope\:(5.5)(4.2)
laplacetransform sin(kt)	laplacetransform\:\sin(kt)
derivative of 1/(x^{11)}	derivative\:\frac{1}{x^{11}}
f(x)=sqrt(xe^x)	f(x)=\sqrt{xe^{x}}
(dx)/(dt)=4000-x/(50+t)	\frac{dx}{dt}=4000-\frac{x}{50+t}
tangent of (x^2+1)/(x^2+1+x)	tangent\:\frac{x^{2}+1}{x^{2}+1+x}
derivative of ln(x^2-9x+1)	\frac{d}{dx}(\ln(x^{2}-9x+1))
integral of 1/(sqrt(x^2-6x+10))	\int\:\frac{1}{\sqrt{x^{2}-6x+10}}dx
integral of x^2-2x-15	\int\:x^{2}-2x-15dx
derivative of (2e^x/(5x))	\frac{d}{dx}(\frac{2e^{x}}{5x})
integral of sin(2θ)cos^4(2θ)	\int\:\sin(2θ)\cos^{4}(2θ)dθ
integral of 1/(sec(θ))	\int\:\frac{1}{\sec(θ)}dθ
d/(dt)(tcos(t))	\frac{d}{dt}(t\cos(t))
derivative of xe^{xsin(x})	\frac{d}{dx}(xe^{x\sin(x)})
integral of (sin(u))/u	\int\:\frac{\sin(u)}{u}du
2y^{''}-16y^'+32y=4e^{4t}	2y^{\prime\:\prime\:}-16y^{\prime\:}+32y=4e^{4t}
tangent of 4x^2+3x	tangent\:4x^{2}+3x
(dy)/(dx)=4x-6	\frac{dy}{dx}=4x-6
(\partial)/(\partial y)(sqrt(2x-3y))	\frac{\partial\:}{\partial\:y}(\sqrt{2x-3y})
derivative of (2tan^2(2x-1)^{1/2})	\frac{d}{dx}((2\tan^{2}(2x)-1)^{\frac{1}{2}})
d/(du)(sqrt(u^2+v^2))	\frac{d}{du}(\sqrt{u^{2}+v^{2}})
sum from n=1 to infinity of ((-3)^n)/(7^{n+1)}	\sum\:_{n=1}^{\infty\:}\frac{(-3)^{n}}{7^{n+1}}
integral of 8(y^4+4y^2+1)^2(y^3+2y)	\int\:8(y^{4}+4y^{2}+1)^{2}(y^{3}+2y)dy
join ae^v+b/v+c/(v^2)	join\:ae^{v}+\frac{b}{v}+\frac{c}{v^{2}}
tangent of (sqrt(x))/(6x+4)	tangent\:\frac{\sqrt{x}}{6x+4}
derivative of 3csc(x+5/x)	\frac{d}{dx}(3\csc(x)+\frac{5}{x})
limit as x approaches 0 of cos(x)x	\lim\:_{x\to\:0}(\cos(x)x)
d/(dθ)(4-sin(θ))	\frac{d}{dθ}(4-\sin(θ))
integral of 1/(sqrt(21-4x-x^2))	\int\:\frac{1}{\sqrt{21-4x-x^{2}}}dx
laplacetransform xe^x	laplacetransform\:xe^{x}
xy^'+y=-5xy^2,y(1)=3	xy^{\prime\:}+y=-5xy^{2},y(1)=3
derivative of (60t^2)/(t^2+150)	derivative\:\frac{60t^{2}}{t^{2}+150}
derivative of cos(pi/x)	\frac{d}{dx}(\cos(\frac{π}{x}))
limit as x approaches 0 of (cos(3x))/x	\lim\:_{x\to\:0}(\frac{\cos(3x)}{x})
derivative of e^{-x}cos(sqrt(x))	\frac{d}{dx}(e^{-x}\cos(\sqrt{x}))
(dy)/(dx)=(y^2+1)/(x^2+1)	\frac{dy}{dx}=\frac{y^{2}+1}{x^{2}+1}
parity y=cos(tan(x))	parity\:y=\cos(\tan(x))
area 4/x ,16x, 1/16 x	area\:\frac{4}{x},16x,\frac{1}{16}x
integral of (sin(2x))/(1+cos^2(x))	\int\:\frac{\sin(2x)}{1+\cos^{2}(x)}dx
integral of (x^2+1)/((x+1)^2)e^x	\int\:\frac{x^{2}+1}{(x+1)^{2}}e^{x}dx
limit as x approaches 1+of x^2-4x+3	\lim\:_{x\to\:1+}(x^{2}-4x+3)
(\partial}{\partial x}(4e^{\frac{x^2)/y}-cos(xy^3))	\frac{\partial\:}{\partial\:x}(4e^{\frac{x^{2}}{y}}-\cos(xy^{3}))
limit as x approaches 0 of 4sqrt(x)+x	\lim\:_{x\to\:0}(4\sqrt{x}+x)
integral of 2x^7+4x^6+x^5+1	\int\:2x^{7}+4x^{6}+x^{5}+1dx
tangent of y=2x^3-2x,(-1,0)	tangent\:y=2x^{3}-2x,(-1,0)
derivative of cos^2(5pix)	derivative\:\cos^{2}(5πx)
derivative of (5ln(4x))/(2-3x)	derivative\:\frac{5\ln(4x)}{2-3x}
integral of pi/(200)sin((pix)/(100))	\int\:\frac{π}{200}\sin(\frac{πx}{100})dx
derivative of-sin(pixpi)	\frac{d}{dx}(-\sin(πx)π)
derivative of y=2x^{-3}	derivative\:y=2x^{-3}
integral of x\sqrt[3]{x^2-9}	\int\:x\sqrt[3]{x^{2}-9}dx
(dy)/(dx)=(1/(sqrt(1+x^2)))	\frac{dy}{dx}=(\frac{1}{\sqrt{1+x^{2}}})
limit as x approaches 4-of (x-10)/(x-4)	\lim\:_{x\to\:4-}(\frac{x-10}{x-4})
(\partial)/(\partial y)(1/(2-x+y))	\frac{\partial\:}{\partial\:y}(\frac{1}{2-x+y})
limit as x approaches-1 of x^3-3x^2-2x+1	\lim\:_{x\to\:-1}(x^{3}-3x^{2}-2x+1)
expand x^2(1-2x)	expand\:x^{2}(1-2x)
derivative of 1/(csc(x))	\frac{d}{dx}(\frac{1}{\csc(x)})
integral from 0 to 2 of (2x-x^3)	\int\:_{0}^{2}(2x-x^{3})dx
(\partial)/(\partial x)(x^6y^5+2x^9y)	\frac{\partial\:}{\partial\:x}(x^{6}y^{5}+2x^{9}y)
(dy)/(dx)=10sqrt(y)	\frac{dy}{dx}=10\sqrt{y}
y^'+1/2y= 3/2t	y^{\prime\:}+\frac{1}{2}\cdot\:y=\frac{3}{2}\cdot\:t

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