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Popular Calculus Problems

derivative of 3x^{-3}	\frac{d}{dx}(3x^{-3})
derivative of f(x)=(4x+3)/(4x-3)	derivative\:f(x)=\frac{4x+3}{4x-3}
slope ofintercept (-2,7),(0,5)	slopeintercept\:(-2,7),(0,5)
d/(dv)(sqrt(u/v))	\frac{d}{dv}(\sqrt{\frac{u}{v}})
(\partial)/(\partial y)(-xe^{-3xy})	\frac{\partial\:}{\partial\:y}(-xe^{-3xy})
integral of xe^{mx}	\int\:xe^{mx}dx
limit as x approaches 0 of (e^{5x}-1)/x	\lim\:_{x\to\:0}(\frac{e^{5x}-1}{x})
integral of cos(5x)sin(x)sin(8x)	\int\:\cos(5x)\sin(x)\sin(8x)dx
(dy)/(dx)=(xcos(x^2))/(4y)	\frac{dy}{dx}=\frac{x\cos(x^{2})}{4y}
derivative of 48x^{1/2}	\frac{d}{dx}(48x^{\frac{1}{2}})
f(x)= 2/(ln(x))	f(x)=\frac{2}{\ln(x)}
derivative of ((1-cos(x)/(1+cos(x)))^3)	\frac{d}{dx}((\frac{1-\cos(x)}{1+\cos(x)})^{3})
limit as x approaches 0 of (5-5sin(x))/x	\lim\:_{x\to\:0}(\frac{5-5\sin(x)}{x})
limit as x approaches-pi/2-of sec(x)	\lim\:_{x\to\:-\frac{π}{2}-}(\sec(x))
derivative of tanh(x^2-9)	\frac{d}{dx}(\tanh(x^{2}-9))
limit as x approaches 7 of x^4	\lim\:_{x\to\:7}(x^{4})
sum from n=1 to infinity}(((-1)^{(n-1) of))/(((2n-1)^3))	\sum\:_{n=1}^{\infty\:}\frac{((-1)^{(n-1)})}{((2n-1)^{3})}
integral of (x^2-4x+5)/((x^2-1)(x+3))	\int\:\frac{x^{2}-4x+5}{(x^{2}-1)(x+3)}dx
integral from 1 to 4 of xln(x)	\int\:_{1}^{4}x\ln(x)dx
tangent of f(x)=2x^2-9x+10,\at x=1	tangent\:f(x)=2x^{2}-9x+10,\at\:x=1
y^'+1/x y= 2/3 x^4y^4	y^{\prime\:}+\frac{1}{x}y=\frac{2}{3}x^{4}y^{4}
derivative of 7e^xcsc(x)	\frac{d}{dx}(7e^{x}\csc(x))
derivative of (1-3x+x^3)/(x^3)	derivative\:\frac{1-3x+x^{3}}{x^{3}}
integral from 0 to pi of sin(mx)e^{nx}	\int\:_{0}^{π}\sin(mx)e^{nx}dx
integral of sin((xpi)/2)	\int\:\sin(\frac{xπ}{2})dx
integral of ((x-1)^3)/(x^2)	\int\:\frac{(x-1)^{3}}{x^{2}}dx
laplacetransform g(t)=4cos(4t)-9sin(4t)+2cos(10t)	laplacetransform\:g(t)=4\cos(4t)-9\sin(4t)+2\cos(10t)
(\partial)/(\partial x)(rsin(t)sin(x))	\frac{\partial\:}{\partial\:x}(r\sin(t)\sin(x))
(\partial)/(\partial x)(e^{-(x^2+y^2+2z^2)})	\frac{\partial\:}{\partial\:x}(e^{-(x^{2}+y^{2}+2z^{2})})
integral of 3/(sqrt(x))+(xsqrt(x))/4+C	\int\:\frac{3}{\sqrt{x}}+\frac{x\sqrt{x}}{4}+Cdx
integral of (x-1)/(x^2-x-1)	\int\:\frac{x-1}{x^{2}-x-1}dx
tangent of 3x^3-6x^2+4x+21	tangent\:3x^{3}-6x^{2}+4x+21
limit as x approaches 0 of (18)/(x^2)	\lim\:_{x\to\:0}(\frac{18}{x^{2}})
(\partial)/(\partial x)(3x^2-24y)	\frac{\partial\:}{\partial\:x}(3x^{2}-24y)
derivative of (x-1^{1/3}(x+2)^{2/3})	\frac{d}{dx}((x-1)^{\frac{1}{3}}(x+2)^{\frac{2}{3}})
(dy}{dx}+\frac{x^2)/y =0	\frac{dy}{dx}+\frac{x^{2}}{y}=0
limit as x approaches 0 of x^{21x}	\lim\:_{x\to\:0}(x^{21x})
(dy)/(dx)=(x-y)/(x+2y)	\frac{dy}{dx}=\frac{x-y}{x+2y}
(9+x)(dy)/(dx)=6+x	(9+x)\frac{dy}{dx}=6+x
derivative of (xy/2)	\frac{d}{dx}(\frac{xy}{2})
ty^'-3y=t^4	t\cdot\:y^{\prime\:}-3\cdot\:y=t^{4}
laplacetransform (t+2)^2e^t	laplacetransform\:(t+2)^{2}e^{t}
f(x)=x^3e^x	f(x)=x^{3}e^{x}
derivative of x^3+y^2	\frac{d}{dx}(x^{3}+y^{2})
(\partial)/(\partial x)(2e^{x^2})	\frac{\partial\:}{\partial\:x}(2e^{x^{2}})
tangent of ((2x-1)/(x+1)),2	tangent\:(\frac{2x-1}{x+1}),2
(dy)/(dx)=e^{2x}+3y	\frac{dy}{dx}=e^{2x}+3y
integral of xsqrt(16+x^2)	\int\:x\sqrt{16+x^{2}}dx
f(x)=ln(1+1/x)	f(x)=\ln(1+\frac{1}{x})
(x/(sqrt(x^2+1)))^'	(\frac{x}{\sqrt{x^{2}+1}})^{\prime\:}
integral from-infinity to 2 of xe^x	\int\:_{-\infty\:}^{2}xe^{x}dx
derivative of 6x^2y-3xy^2	\frac{d}{dx}(6x^{2}y-3xy^{2})
integral of (5x^3)	\int\:(5x^{3})dx
tangent of f(x)=-6/((3x+5)^2),\at x=-1	tangent\:f(x)=-\frac{6}{(3x+5)^{2}},\at\:x=-1
integral of (x^3)/(x^4-2)	\int\:\frac{x^{3}}{x^{4}-2}dx
d/(d{y)}(({y})/({z)})	\frac{d}{d{y}}(\frac{{y}}{{z}})
derivative of 4x^3-12x	\frac{d}{dx}(4x^{3}-12x)
integral from 1 to e of ((1+ln(x))^2)/x	\int\:_{1}^{e}\frac{(1+\ln(x))^{2}}{x}dx
integral from 1 to 5 of 6250pix	\int\:_{1}^{5}6250πxdx
tangent of 2sqrt(x),\at x=9	tangent\:2\sqrt{x},\at\:x=9
integral of 4sin(5x)	\int\:4\sin(5x)dx
sum from n=0 to infinity of n(6/7)^n	\sum\:_{n=0}^{\infty\:}n(\frac{6}{7})^{n}
f(x)=x^3+2	f(x)=x^{3}+2
derivative of x-10	\frac{d}{dx}(x-10)
tangent of y=6e^xcos(x),(0,6)	tangent\:y=6e^{x}\cos(x),(0,6)
derivative of 3ln(x^2)	\frac{d}{dx}(3\ln(x^{2}))
tangent of e^x,\at x=5	tangent\:e^{x},\at\:x=5
derivative of (3x-1^5)	\frac{d}{dx}((3x-1)^{5})
derivative of sin(2x)cos(3x)	derivative\:\sin(2x)\cos(3x)
integral of x^2e^xcos(x)	\int\:x^{2}e^{x}\cos(x)dx
integral of 2xcos(x^2)	\int\:2x\cos(x^{2})dx
integral from-1 to 2 of (3x^2-2x+3)	\int\:_{-1}^{2}(3x^{2}-2x+3)dx
sum from n=0 to infinity of 1-(0.2)^n	\sum\:_{n=0}^{\infty\:}1-(0.2)^{n}
derivative of 4x^{-2x}	\frac{d}{dx}(4x^{-2x})
integral of 1/(x(100-x))	\int\:\frac{1}{x(100-x)}dx
derivative of sqrt(1+x+x^2)	\frac{d}{dx}(\sqrt{1+x+x^{2}})
derivative of f(x)= 1/(sqrt(x^{17))}	derivative\:f(x)=\frac{1}{\sqrt{x^{17}}}
inverse oflaplace 1/((s-1)(s^2+9))	inverselaplace\:\frac{1}{(s-1)(s^{2}+9)}
area 2x^2-8x-55,-x^2-2x+50,-5,7	area\:2x^{2}-8x-55,-x^{2}-2x+50,-5,7
(\partial)/(\partial y)(e^{xz}y^3-ln(x))	\frac{\partial\:}{\partial\:y}(e^{xz}y^{3}-\ln(x))
integral of x(x+3)^7	\int\:x(x+3)^{7}dx
x^2(dy)/(dx)=sqrt(y)(4x+3)	x^{2}\frac{dy}{dx}=\sqrt{y}(4x+3)
(\partial)/(\partial x)(-sin(xy))	\frac{\partial\:}{\partial\:x}(-\sin(xy))
integral of x/((x^2-1))	\int\:\frac{x}{(x^{2}-1)}dx
integral of 8x^2ln(x)	\int\:8x^{2}\ln(x)dx
d/(dt)(sin(t)+cos(t))	\frac{d}{dt}(\sin(t)+\cos(t))
area y=x^3,(-1,2)	area\:y=x^{3},(-1,2)
integral of (x^3+x)^2	\int\:(x^{3}+x)^{2}dx
integral of cos(4y)	\int\:\cos(4y)dy
y^'+1/t y=0	y^{\prime\:}+\frac{1}{t}y=0
slope of (4.4)(5.9)	slope\:(4.4)(5.9)
derivative of 1/3 x^3+1/2 x^2+2	\frac{d}{dx}(\frac{1}{3}x^{3}+\frac{1}{2}x^{2}+2)
y^{''}-2/x y^'-(10)/(x^2)=0	y^{\prime\:\prime\:}-\frac{2}{x}y^{\prime\:}-\frac{10}{x^{2}}=0
integral of (26)/((x-1)(x^2+25))	\int\:\frac{26}{(x-1)(x^{2}+25)}dx
integral of (2x-3)/(sqrt(4x-x^2))	\int\:\frac{2x-3}{\sqrt{4x-x^{2}}}dx
integral from e to e^2 of 1/(xln(x))	\int\:_{e}^{e^{2}}\frac{1}{x\ln(x)}dx
derivative of (40/(1+79e^{-x)})	\frac{d}{dx}(\frac{40}{1+79e^{-x}})
derivative of x/(sqrt(x-7))	\frac{d}{dx}(\frac{x}{\sqrt{x-7}})
integral of (2x-1)/(4x^2-1)	\int\:\frac{2x-1}{4x^{2}-1}dx
(\partial)/(\partial y)(5xy^2)	\frac{\partial\:}{\partial\:y}(5xy^{2})

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