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Popular Calculus Problems

derivative of (x^3)/9	derivative\:\frac{x^{3}}{9}
(sin(xy)+xycos(xy))dx+(x^2cos(xy))dy=0	(\sin(xy)+xy\cos(xy))dx+(x^{2}\cos(xy))dy=0
limit as x approaches 2+of (x^2+1)/(x-2)	\lim\:_{x\to\:2+}(\frac{x^{2}+1}{x-2})
integral from 1 to infinity of e^{-11x}	\int\:_{1}^{\infty\:}e^{-11x}dx
derivative of y=e^{-x}ln(x)	derivative\:y=e^{-x}\ln(x)
limit as x approaches 3+of 1/(3-x)	\lim\:_{x\to\:3+}(\frac{1}{3-x})
integral of 1/(sqrt(x^2+2^2))	\int\:\frac{1}{\sqrt{x^{2}+2^{2}}}dx
(\partial)/(\partial x)(ln(x-6y))	\frac{\partial\:}{\partial\:x}(\ln(x-6y))
integral of 2cos(1/2 x)	\int\:2\cos(\frac{1}{2}x)dx
(\partial)/(\partial y)(4x^3y^2-2xy^3)	\frac{\partial\:}{\partial\:y}(4x^{3}y^{2}-2xy^{3})
derivative of x^3+7e^x	derivative\:x^{3}+7e^{x}
(xdy)/(dx)=y^2-4	\frac{xdy}{dx}=y^{2}-4
(dy)/(dx)=(y/x+1/4)^2	\frac{dy}{dx}=(\frac{y}{x}+\frac{1}{4})^{2}
tangent of y=(f(x))^2,\at x=0	tangent\:y=(f(x))^{2},\at\:x=0
derivative of 4500(1-1/50 t)^2	derivative\:4500(1-\frac{1}{50}t)^{2}
integral of (2x^2+8x-8)/(x-4)	\int\:\frac{2x^{2}+8x-8}{x-4}dx
derivative of f(x)=((x-2)^5)/(16)	derivative\:f(x)=\frac{(x-2)^{5}}{16}
limit as x approaches infinity of (2x^3-5x+4)/(x^2+3x-4)	\lim\:_{x\to\:\infty\:}(\frac{2x^{3}-5x+4}{x^{2}+3x-4})
maclaurin xcos(x)	maclaurin\:x\cos(x)
integral of 9/(x^2-6x+18)	\int\:\frac{9}{x^{2}-6x+18}dx
inverse oflaplace (0.6)/s	inverselaplace\:\frac{0.6}{s}
integral from-1 to 0 of-1	\int\:_{-1}^{0}-1dx
integral of cos((npix)/L)sin((npix)/L)	\int\:\cos(\frac{nπx}{L})\sin(\frac{nπx}{L})dx
tangent of f(x)=(20)/(sqrt(x-1)),\at x=5	tangent\:f(x)=\frac{20}{\sqrt{x-1}},\at\:x=5
laplacetransform t^2t^3	laplacetransform\:t^{2}t^{3}
integral from 0 to infinity of xe^{-2x}	\int\:_{0}^{\infty\:}xe^{-2x}dx
integral of (-4xy+2x^3-2y+3)	\int\:(-4xy+2x^{3}-2y+3)dx
integral of (sin(wt))^2	\int\:(\sin(wt))^{2}dt
integral of (2^x+e^x)	\int\:(2^{x}+e^{x})dx
integral from-3 to 3 of (14)/(x^2-6x-40)	\int\:_{-3}^{3}\frac{14}{x^{2}-6x-40}dx
(\partial}{\partial x}(\frac{(y^3))/x)	\frac{\partial\:}{\partial\:x}(\frac{(y^{3})}{x})
tangent of y=x^2+x,(0,0)	tangent\:y=x^{2}+x,(0,0)
integral from 0 to 1 of (22)/(4y-1)	\int\:_{0}^{1}\frac{22}{4y-1}dy
derivative of (x^2-1/(x^2-4))	\frac{d}{dx}(\frac{x^{2}-1}{x^{2}-4})
integral of (cos(y))/(sin^2(y))	\int\:\frac{\cos(y)}{\sin^{2}(y)}dy
(\partial)/(\partial x)(5e^y)	\frac{\partial\:}{\partial\:x}(5e^{y})
sum from n=1 to infinity of 1/((n^2+8n))	\sum\:_{n=1}^{\infty\:}\frac{1}{(n^{2}+8n)}
integral of 1/(x(1+ln(x))(2+ln(x)))	\int\:\frac{1}{x(1+\ln(x))(2+\ln(x))}dx
integral of (8+5x)/(1+x^2)	\int\:\frac{8+5x}{1+x^{2}}dx
limit as x approaches-10-of 1/(x+10)	\lim\:_{x\to\:-10-}(\frac{1}{x+10})
derivative of tan(4x^5sec(2x^3))	\frac{d}{dx}(\tan(4x^{5})\sec(2x^{3}))
integral of pi^2-x^2	\int\:π^{2}-x^{2}dx
integral of 8/(1+8x)	\int\:\frac{8}{1+8x}dx
derivative of (3x^2^{2x}*(x^2+2x)^2)	\frac{d}{dx}((3x^{2})^{2x}\cdot\:(x^{2}+2x)^{2})
integral of (2x)/((x-1)(x-3))	\int\:\frac{2x}{(x-1)(x-3)}dx
integral of tan^3(θ)sec^4(θ)	\int\:\tan^{3}(θ)\sec^{4}(θ)dθ
integral of (4-x^3-5x^5)	\int\:(4-x^{3}-5x^{5})dx
limit as x approaches 0+of tan^x(6x)	\lim\:_{x\to\:0+}(\tan^{x}(6x))
limit as x approaches 0 of e^1	\lim\:_{x\to\:0}(e^{1})
integral of x^3sqrt(x^2+44)	\int\:x^{3}\sqrt{x^{2}+44}dx
limit as x approaches 0 of ((cos(ax)-cos(bx)))/(x^2)	\lim\:_{x\to\:0}(\frac{(\cos(ax)-\cos(bx))}{x^{2}})
derivative of (sqrt(2x^2)/(cos(x)))	\frac{d}{dx}(\frac{\sqrt{2x^{2}}}{\cos(x)})
derivative of ln^4(x)	\frac{d}{dx}(\ln^{4}(x))
inverse oflaplace (s+2)/(s(s+1)^2)	inverselaplace\:\frac{s+2}{s(s+1)^{2}}
derivative of g(t)=2t^{-3/4}	derivative\:g(t)=2t^{-\frac{3}{4}}
(\partial)/(\partial x)(e^x+yz)	\frac{\partial\:}{\partial\:x}(e^{x}+yz)
3xy^'-y(x+1)+7y^4=0	3xy^{\prime\:}-y(x+1)+7y^{4}=0
implicit (dy)/(dx),x^2+y^2=24	implicit\:\frac{dy}{dx},x^{2}+y^{2}=24
derivative of cos^2(t)	derivative\:\cos^{2}(t)
derivative of tan^6(x)	derivative\:\tan^{6}(x)
limit as h approaches 0 of cos(3/h)	\lim\:_{h\to\:0}(\cos(\frac{3}{h}))
integral of 6θsec^2(θ)	\int\:6θ\sec^{2}(θ)dθ
integral of t^6	\int\:t^{6}dt
f(x)=(sin(1/x)*x^3)/(ln(x))	f(x)=\frac{\sin(\frac{1}{x})\cdot\:x^{3}}{\ln(x)}
d/(dt)(e^{-at})	\frac{d}{dt}(e^{-at})
integral of 1/((49-x^2)^{3/2)}	\int\:\frac{1}{(49-x^{2})^{\frac{3}{2}}}dx
derivative of f(x)=arccos(2x)	derivative\:f(x)=\arccos(2x)
slope ofintercept (-10,-7),(-5,-9)	slopeintercept\:(-10,-7),(-5,-9)
domain of f(x)=arctan((2x)/(1-x^2))	domain\:f(x)=\arctan(\frac{2x}{1-x^{2}})
integral of (\sqrt[4]{x^5})	\int\:(\sqrt[4]{x^{5}})dx
(\partial)/(\partial s)(1+st)	\frac{\partial\:}{\partial\:s}(1+st)
integral of (11x+64)/(x^2+13x+40)	\int\:\frac{11x+64}{x^{2}+13x+40}dx
limit as x approaches 0 of ((x^2))/(e-1)	\lim\:_{x\to\:0}(\frac{(x^{2})}{e-1})
(\partial)/(\partial x)(1-x^2-x-2y^2+y)	\frac{\partial\:}{\partial\:x}(1-x^{2}-x-2y^{2}+y)
derivative of ln(2)+ln(x)	derivative\:\ln(2)+\ln(x)
derivative of y=(e^{6x})/(e^{6x)+3}	derivative\:y=\frac{e^{6x}}{e^{6x}+3}
(\partial)/(\partial x)(e^{-3y}cos(pix))	\frac{\partial\:}{\partial\:x}(e^{-3y}\cos(πx))
6y^{''}-y^'-2y=0	6y^{\prime\:\prime\:}-y^{\prime\:}-2y=0
integral of (1+sin(x))/(1+cos(x))	\int\:\frac{1+\sin(x)}{1+\cos(x)}dx
(\partial}{\partial x}(\frac{(y-3x))/z)	\frac{\partial\:}{\partial\:x}(\frac{(y-3x)}{z})
tangent of f(x)=x^2+8,(-3,17)	tangent\:f(x)=x^{2}+8,(-3,17)
integral from 2 to 7 of 1/(x^2-1)	\int\:_{2}^{7}\frac{1}{x^{2}-1}dx
tangent of y=(6x)/(x+2)	tangent\:y=\frac{6x}{x+2}
derivative of (1+5x(1-7x))	\frac{d}{dx}((1+5x)(1-7x))
derivative of (log_{e}(x)^x)	\frac{d}{dx}((\log_{e}(x))^{x})
y^{''}+7y^'+10y=0,y(0)=1,y^'(0)=0	y^{\prime\:\prime\:}+7y^{\prime\:}+10y=0,y(0)=1,y^{\prime\:}(0)=0
integral of 1/(sqrt(x)-5\sqrt[3]{x)}	\int\:\frac{1}{\sqrt{x}-5\sqrt[3]{x}}dx
limit as x approaches 0 of 2/(3+4^{1/x)}	\lim\:_{x\to\:0}(\frac{2}{3+4^{\frac{1}{x}}})
area y=x^3+1,(-1,2)	area\:y=x^{3}+1,(-1,2)
(\partial)/(\partial x)(yx-ln(x^3y+6x))	\frac{\partial\:}{\partial\:x}(yx-\ln(x^{3}y+6x))
(\partial)/(\partial x)((x-y)e^{y+2x^2})	\frac{\partial\:}{\partial\:x}((x-y)e^{y+2x^{2}})
integral of e^{sin(x)}7cos(x)	\int\:e^{\sin(x)}7\cos(x)dx
derivative of-2/((1+x^2))	\frac{d}{dx}(-\frac{2}{(1+x)^{2}})
d/(d{x)}(({x}^2+{y}^2+{z}^2)^{(-1)/2})	\frac{d}{d{x}}(({x}^{2}+{y}^{2}+{z}^{2})^{\frac{-1}{2}})
limit as x approaches 0+of xln(x^5)	\lim\:_{x\to\:0+}(x\ln(x^{5}))
derivative of (x+3/(2x^2e^x))	\frac{d}{dx}(\frac{x+3}{2x^{2}e^{x}})
slope of x^2+y^2=27,\at x=3	slope\:x^{2}+y^{2}=27,\at\:x=3
integral of xsin(sqrt(x^2+4))	\int\:x\sin(\sqrt{x^{2}+4})dx
derivative of (sqrt(x)+1)^{81}	derivative\:(\sqrt{x}+1)^{81}
derivative of (e^{2x})/(ln(6x))	derivative\:\frac{e^{2x}}{\ln(6x)}

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