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Popular Calculus Problems

derivative of 11	\frac{d}{dx}(11)
integral of e^{cos(t)}sin(2t)	\int\:e^{\cos(t)}\sin(2t)dt
derivative of 1/6 ln(e^{2x}-e^x+1)	\frac{d}{dx}(\frac{1}{6}\ln(e^{2x}-e^{x}+1))
derivative of xsqrt(h(x))	derivative\:x\sqrt{h(x)}
inverse oflaplace 1/(s^2(s^2+2^2))	inverselaplace\:\frac{1}{s^{2}(s^{2}+2^{2})}
y^'+6xy=0	y^{\prime\:}+6xy=0
laplacetransform 2t-e^{-3t}	laplacetransform\:2t-e^{-3t}
integral of (x^2e^{3x})	\int\:(x^{2}e^{3x})dx
(\partial)/(\partial v)(1/3 (u+v))	\frac{\partial\:}{\partial\:v}(\frac{1}{3}(u+v))
d/(dz)(4-z)	\frac{d}{dz}(4-z)
y^{''}+2y^'=sin(sqrt(2)t)	y^{\prime\:\prime\:}+2y^{\prime\:}=\sin(\sqrt{2}t)
integral from 0 to 3 of (5x-x^2)-(2x)	\int\:_{0}^{3}(5x-x^{2})-(2x)dx
(d^2)/(dx^2)(-(2x^2)/(5y^2))	\frac{d^{2}}{dx^{2}}(-\frac{2x^{2}}{5y^{2}})
(dy)/(dx)=e^{6y+10x}	\frac{dy}{dx}=e^{6y+10x}
derivative of 2x-(16/(x^2))	\frac{d}{dx}(2x-\frac{16}{x^{2}})
integral from 0 to 6 of 2x+1	\int\:_{0}^{6}2x+1dx
d/(dt)(-t)	\frac{d}{dt}(-t)
x^2-2xy+x(dy)/(dx)=0	x^{2}-2xy+x\frac{dy}{dx}=0
(d^2)/(dx^2)(16x^3-34x^2)	\frac{d^{2}}{dx^{2}}(16x^{3}-34x^{2})
derivative of xy= derivative of 4	\frac{d}{dx}(xy)=\frac{d}{dx}(4)
derivative of f(x)=(arccos(x))^3	derivative\:f(x)=(\arccos(x))^{3}
integral of cos(3x+2)	\int\:\cos(3x+2)dx
tangent of f(x)=4(x-1/x)^3,\at x=2	tangent\:f(x)=4(x-\frac{1}{x})^{3},\at\:x=2
tangent of y=(-2x)/(x^2+1),(0,0)	tangent\:y=\frac{-2x}{x^{2}+1},(0,0)
limit as x approaches 0 of x/(csc^2(x))	\lim\:_{x\to\:0}(\frac{x}{\csc^{2}(x)})
limit as x approaches 5 of x^2-2x+1	\lim\:_{x\to\:5}(x^{2}-2x+1)
derivative of \sqrt[3]{x^2}+2sqrt(x^3)	\frac{d}{dx}(\sqrt[3]{x^{2}}+2\sqrt{x^{3}})
(\partial)/(\partial x)(5e^{yz}cos(xyz))	\frac{\partial\:}{\partial\:x}(5e^{yz}\cos(xyz))
area x^2-8x+15,0	area\:x^{2}-8x+15,0
(\partial)/(\partial y)(yx)	\frac{\partial\:}{\partial\:y}(yx)
tangent of f(x)=6x^2-4x+4,(1,6)	tangent\:f(x)=6x^{2}-4x+4,(1,6)
derivative of y= 3/(e^x+e^{-x)}	derivative\:y=\frac{3}{e^{x}+e^{-x}}
derivative of 3x,-2y,x-y	\frac{d}{dx}(3x,-2y,x-y)
derivative of (e^{-x^2}(-2x))	\frac{d}{dx}((e^{-x^{2}})(-2x))
y^{''}+y=-sin(2x),y(0)=0,y^'(0)=0	y^{\prime\:\prime\:}+y=-\sin(2x),y(0)=0,y^{\prime\:}(0)=0
integral of 1/((x^2+1)(x+1))	\int\:\frac{1}{(x^{2}+1)(x+1)}dx
integral of ((9+x+x^2))/(sqrt(x))	\int\:\frac{(9+x+x^{2})}{\sqrt{x}}dx
derivative of cos(2xsin(x))	\frac{d}{dx}(\cos(2x)\sin(x))
integral of t^5-7t	\int\:t^{5}-7tdt
(\partial)/(\partial x)(2x^2+4y^2+1)	\frac{\partial\:}{\partial\:x}(2x^{2}+4y^{2}+1)
derivative of 2^{x^3+3x}	\frac{d}{dx}(2^{x^{3}+3x})
tan(t)y^'-y=1	\tan(t)y^{\prime\:}-y=1
integral of x^2sqrt(x^2-9)	\int\:x^{2}\sqrt{x^{2}-9}dx
y^{''}+4y=10x(4-x),y(0)=-5,y(4)=10	y^{\prime\:\prime\:}+4y=10x(4-x),y(0)=-5,y(4)=10
d/(dt)(t^3+3t)	\frac{d}{dt}(t^{3}+3t)
(\partial)/(\partial x)(ytan(x))	\frac{\partial\:}{\partial\:x}(y\tan(x))
integral of-25cos(5t+pi)	\int\:-25\cos(5t+π)dt
integral of 3e^2	\int\:3e^{2}dx
derivative of (x^2+4/(4-x^2))	\frac{d}{dx}(\frac{x^{2}+4}{4-x^{2}})
y^'=y-x^2	y^{\prime\:}=y-x^{2}
derivative of arcsin(x^3)	derivative\:\arcsin(x^{3})
f(x)=sqrt(7-x^3)	f(x)=\sqrt{7-x^{3}}
integral from 0 to 7 of 2x\sqrt[3]{x+1}	\int\:_{0}^{7}2x\sqrt[3]{x+1}dx
integral of 1/(sin^5(x))	\int\:\frac{1}{\sin^{5}(x)}dx
derivative of f(x)=sqrt(x)+1/(sqrt(x^3))	derivative\:f(x)=\sqrt{x}+\frac{1}{\sqrt{x^{3}}}
area x=2y,x=y^2-3	area\:x=2y,x=y^{2}-3
integral of 2x^2+5x	\int\:2x^{2}+5xdx
(dy)/(dx)=(e^x)/(e^y)	\frac{dy}{dx}=\frac{e^{x}}{e^{y}}
tangent of y=x^4+4x^2-x,(1,4)	tangent\:y=x^{4}+4x^{2}-x,(1,4)
tangent of y= 1/3 x^3-3x^2+5x	tangent\:y=\frac{1}{3}x^{3}-3x^{2}+5x
integral of x*\sqrt[3]{x-4}	\int\:x\cdot\:\sqrt[3]{x-4}dx
derivative of (x^2-1)/(x^2)	derivative\:\frac{x^{2}-1}{x^{2}}
limit as x approaches 0 of ((4+x)^{-1}-4^{-1})/x	\lim\:_{x\to\:0}(\frac{(4+x)^{-1}-4^{-1}}{x})
derivative of 2^2	derivative\:2^{2}
integral of xarctan^2(x)	\int\:x\arctan^{2}(x)dx
(\partial ^2)/(\partial x\partial y)(xy+8/x+8/y)	\frac{\partial\:^{2}}{\partial\:x\partial\:y}(xy+\frac{8}{x}+\frac{8}{y})
integral of 28tan^6(x)	\int\:28\tan^{6}(x)dx
limit as x approaches pi of x/pi	\lim\:_{x\to\:π}(\frac{x}{π})
derivative of x+sqrt(x+5)	\frac{d}{dx}(x+\sqrt{x+5})
integral of (e^{2x}+3)^2	\int\:(e^{2x}+3)^{2}dx
area (152)/x ,-49x+189	area\:\frac{152}{x},-49x+189
y^{''}-6y^'+5y=0,y(0)=3,y^'(0)=11	y^{\prime\:\prime\:}-6y^{\prime\:}+5y=0,y(0)=3,y^{\prime\:}(0)=11
limit as x approaches-3 of (5x^2+15x)/(x+3)	\lim\:_{x\to\:-3}(\frac{5x^{2}+15x}{x+3})
limit as x approaches pi of ln\|cos(x)-4\|	\lim\:_{x\to\:π}(\ln\left\|\cos(x)-4\right\|)
integral of (((7-2x))/(x^{1/2)}+3(5-e^x+2e^3))	\int\:(\frac{(7-2x)}{x^{\frac{1}{2}}}+3(5-e^{x}+2e^{3}))dx
derivative of x^3e^x	derivative\:x^{3}e^{x}
(\partial)/(\partial x)(e^xx+e^x2y)	\frac{\partial\:}{\partial\:x}(e^{x}x+e^{x}2y)
integral of (sin(npix))/(npi)	\int\:\frac{\sin(nπx)}{nπ}dx
(dy)/(dx)= 1/(x^2+1)	\frac{dy}{dx}=\frac{1}{x^{2}+1}
derivative of-2x^{9/8}	\frac{d}{dx}(-2x^{\frac{9}{8}})
limit as x approaches 30 of 30	\lim\:_{x\to\:30}(30)
integral from 0 to 1 of 8/(sqrt(x)(x+1))	\int\:_{0}^{1}\frac{8}{\sqrt{x}(x+1)}dx
integral from 0 to infinity of 3^{-x}	\int\:_{0}^{\infty\:}3^{-x}dx
integral of x^2(2x+1)	\int\:x^{2}(2x+1)dx
integral of cos(x)e^{-sin(x)}	\int\:\cos(x)e^{-\sin(x)}dx
integral of (9x^2-16x+4)/(x^3-3x^2+2x)	\int\:\frac{9x^{2}-16x+4}{x^{3}-3x^{2}+2x}dx
integral of sec(aθ)tan(aθ)	\int\:\sec(aθ)\tan(aθ)dθ
area y=2,y=x^2-2	area\:y=2,y=x^{2}-2
(\partial)/(\partial y)(x^{1/2}y^{1/2})	\frac{\partial\:}{\partial\:y}(x^{\frac{1}{2}}y^{\frac{1}{2}})
limit as x approaches-2 of 3^{x+1}	\lim\:_{x\to\:-2}(3^{x+1})
derivative of 2x+4	derivative\:2x+4
limit as x approaches 0 of x^2+1	\lim\:_{x\to\:0}(x^{2}+1)
(\partial)/(\partial x)(e^{ysin(x)})	\frac{\partial\:}{\partial\:x}(e^{y\sin(x)})
derivative of 4sqrt(9-x)	\frac{d}{dx}(4\sqrt{9-x})
derivative of (2x/(1+x^2))	\frac{d}{dx}(\frac{2x}{1+x^{2}})
derivative of (1+x^{-1}^2)	\frac{d}{dx}((1+x^{-1})^{2})
derivative of f(x)=log_{2}(3x)	derivative\:f(x)=\log_{2}(3x)
inverse oflaplace (s-1)/(s^2(s+3))	inverselaplace\:\frac{s-1}{s^{2}(s+3)}
limit as t approaches a of t	\lim\:_{t\to\:a}(t)
tangent of x^2-2x	tangent\:x^{2}-2x

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