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Popular Calculus Problems

derivative of (x^3+8e^x)	\frac{d}{dx}((x^{3}+8)e^{x})
derivative of 3^x-3e^pi+x^3	\frac{d}{dx}(3^{x}-3e^{π}+x^{3})
(\partial)/(\partial x)(x^2(e^{-xyz}))	\frac{\partial\:}{\partial\:x}(x^{2}(e^{-xyz}))
derivative of (2x+1(x-5))	\frac{d}{dx}((2x+1)(x-5))
integral of (21pi)/2 cos((21pix)/2)	\int\:\frac{21π}{2}\cos(\frac{21πx}{2})dx
derivative of sqrt(x+2)*sin(x)	\frac{d}{dx}(\sqrt{x+2}\cdot\:\sin(x))
limit as x approaches 0 of 8/(2+e^{1/x)}	\lim\:_{x\to\:0}(\frac{8}{2+e^{\frac{1}{x}}})
derivative of (2cos(x)/(1+sin(x)))	\frac{d}{dx}(\frac{2\cos(x)}{1+\sin(x)})
limit as x approaches infinity of x^2-x	\lim\:_{x\to\:\infty\:}(x^{2}-x)
derivative of f(x)=(12)/(sqrt(x))	derivative\:f(x)=\frac{12}{\sqrt{x}}
derivative of sec^3(sqrt(x))	\frac{d}{dx}(\sec^{3}(\sqrt{x}))
sum from n=1 to infinity of (ln(3))^n	\sum\:_{n=1}^{\infty\:}(\ln(3))^{n}
tangent of f(x)=sqrt(7x+11),(2,5)	tangent\:f(x)=\sqrt{7x+11},(2,5)
y^{''}-4y=e^xcos(x),y(0)=0.7,y^'(0)=-1.5	y^{\prime\:\prime\:}-4y=e^{x}\cos(x),y(0)=0.7,y^{\prime\:}(0)=-1.5
(dy)/(dt)=y^2	\frac{dy}{dt}=y^{2}
derivative of f(x)=ln(6x)	derivative\:f(x)=\ln(6x)
integral of e^{2x}cos(5x)	\int\:e^{2x}\cos(5x)dx
(dy)/(dx)+y=cos(x)	\frac{dy}{dx}+y=\cos(x)
integral of (5sin(2θ))^2	\int\:(5\sin(2θ))^{2}dθ
integral of 1/(x-8sqrt(x)+15)	\int\:\frac{1}{x-8\sqrt{x}+15}dx
integral of (x^2+3x)	\int\:(x^{2}+3x)dx
partialfraction x/(x+2)	partialfraction\:\frac{x}{x+2}
derivative of 1/((1+e^{-x)})	\frac{d}{dx}(\frac{1}{(1+e^{-x})})
integral of (cos(2x))/x	\int\:\frac{\cos(2x)}{x}dx
integral of 2sin(x)+5	\int\:2\sin(x)+5dx
derivative of (e^x)/(x-1)	derivative\:\frac{e^{x}}{x-1}
integral of 3cos(3t)	\int\:3\cos(3t)dt
limit as x approaches 2 of (2x-3)/(x+1)	\lim\:_{x\to\:2}(\frac{2x-3}{x+1})
slope of (3,1),(-2,-2)	slope\:(3,1),(-2,-2)
sum from n=0 to infinity of (nx)^n	\sum\:_{n=0}^{\infty\:}(nx)^{n}
integral of 4/3 x^3	\int\:\frac{4}{3}x^{3}dx
area y=x^2,y=2x+6	area\:y=x^{2},y=2x+6
sin(2x)dx+cos(8y)dy=0,y(pi/2)= pi/8	\sin(2x)dx+\cos(8y)dy=0,y(\frac{π}{2})=\frac{π}{8}
laplacetransform 2cos(3t)	laplacetransform\:2\cos(3t)
integral from 1 to 2 of x^4+1/(4x^4)	\int\:_{1}^{2}x^{4}+\frac{1}{4x^{4}}dx
integral from 0 to 5 of xsqrt(25-x^2)	\int\:_{0}^{5}x\sqrt{25-x^{2}}dx
derivative of 15cos(3t)	derivative\:15\cos(3t)
(5dx)/(dt)=x^2	\frac{5dx}{dt}=x^{2}
sum from n=0 to infinity of q^{2n}	\sum\:_{n=0}^{\infty\:}q^{2n}
limit as x approaches 0 of 1/(x+1)	\lim\:_{x\to\:0}(\frac{1}{x+1})
derivative of x^{0.5}y^{0.5}	\frac{d}{dx}(x^{0.5}y^{0.5})
(\partial)/(\partial x)(3e^{3x+4y}cos(5z))	\frac{\partial\:}{\partial\:x}(3e^{3x+4y}\cos(5z))
(6+x)y^'=5y	(6+x)y^{\prime\:}=5y
integral of 16xln(3x)	\int\:16x\ln(3x)dx
integral of ((1+x))/(1+x^2)	\int\:\frac{(1+x)}{1+x^{2}}dx
area x=-2,x=1,y=2x^2+12,y=0	area\:x=-2,x=1,y=2x^{2}+12,y=0
tangent of f(x)=sqrt(5x+11),(5,6)	tangent\:f(x)=\sqrt{5x+11},(5,6)
f(x)= 3/(x^2)	f(x)=\frac{3}{x^{2}}
derivative of f(x)=sqrt(3)(x^3-x^2)	derivative\:f(x)=\sqrt{3}(x^{3}-x^{2})
integral of (ln(x^3))	\int\:(\ln(x^{3}))dx
integral of 1/(2x-2)	\int\:\frac{1}{2x-2}dx
integral of 2cos^2(4x)sin(4x)	\int\:2\cos^{2}(4x)\sin(4x)dx
(\partial)/(\partial x)((x^2+y^2+z^2)^{1/2})	\frac{\partial\:}{\partial\:x}((x^{2}+y^{2}+z^{2})^{\frac{1}{2}})
limit as x approaches infinity of sec(x)	\lim\:_{x\to\:\infty\:}(\sec(x))
tangent of f(x)=5sqrt(x),\at x=4,x=9	tangent\:f(x)=5\sqrt{x},\at\:x=4,x=9
limit as x approaches-3-of (3-x)/(9-x^2)	\lim\:_{x\to\:-3-}(\frac{3-x}{9-x^{2}})
derivative of (\sqrt[3]{x}/(x-6))	\frac{d}{dx}(\frac{\sqrt[3]{x}}{x-6})
derivative of f(x)=4x^{3/2}	derivative\:f(x)=4x^{\frac{3}{2}}
taylor ln(1-x),0	taylor\:\ln(1-x),0
integral of x(3x+1)^7	\int\:x(3x+1)^{7}dx
laplacetransform (t+5)^3	laplacetransform\:(t+5)^{3}
derivative of (ln(x)/(x^{13)})	\frac{d}{dx}(\frac{\ln(x)}{x^{13}})
derivative of (10)/x	derivative\:\frac{10}{x}
limit as x approaches a of (x-1)/(3x+6)	\lim\:_{x\to\:a}(\frac{x-1}{3x+6})
integral of (sqrt(x)ln(x))	\int\:(\sqrt{x}\ln(x))dx
derivative of pi{r}(x(x)^2h)	\frac{d}{dx}(π{r}(x)(x)^{2}h)
(dy)/(dx)=(3x)/(2y)	\frac{dy}{dx}=\frac{3x}{2y}
integral of e^xln(e^x+1)	\int\:e^{x}\ln(e^{x}+1)dx
integral of (x^2)/((9-x^2)^{-3/2)}	\int\:\frac{x^{2}}{(9-x^{2})^{-\frac{3}{2}}}dx
derivative of 20-20*2^{-x}	\frac{d}{dx}(20-20\cdot\:2^{-x})
derivative of Ae^{5x}	\frac{d}{dx}(Ae^{5x})
y^'-(2/x y)=((y^3)/(x^3)),y(1)=1	y^{\prime\:}-(\frac{2}{x}y)=(\frac{y^{3}}{x^{3}}),y(1)=1
laplacetransform sin(-3t)	laplacetransform\:\sin(-3t)
integral of cos(t)e^{-st}	\int\:\cos(t)e^{-st}dt
limit as x approaches+0 of (sin(x^2))/x	\lim\:_{x\to\:+0}(\frac{\sin(x^{2})}{x})
sum from n=0 to infinity of 7^{-n}	\sum\:_{n=0}^{\infty\:}7^{-n}
derivative of y=(4x^2+x)(x-x^2)	derivative\:y=(4x^{2}+x)(x-x^{2})
derivative of (2+x/(x-1))	\frac{d}{dx}(\frac{2+x}{x-1})
limit as x approaches 3 of+(-1)	\lim\:_{x\to\:3}(+(-1))
d/(dt)(e^{7t}e^{4it})	\frac{d}{dt}(e^{7t}e^{4it})
y^'+2/x y=(1-x)(y^2)	y^{\prime\:}+\frac{2}{x}y=(1-x)(y^{2})
(\partial)/(\partial x)(arctan(xy^2))	\frac{\partial\:}{\partial\:x}(\arctan(xy^{2}))
integral of (1-cos(2x))/2	\int\:\frac{1-\cos(2x)}{2}dx
integral of+x^2sec^2(x^3+1)	\int\:+x^{2}\sec^{2}(x^{3}+1)dx
(\partial)/(\partial x)(x^3(1+y)+z^2)	\frac{\partial\:}{\partial\:x}(x^{3}(1+y)+z^{2})
derivative of (x^2/((5+x)))	\frac{d}{dx}(\frac{x^{2}}{(5+x)})
join arctan(x)-pi/4	join\:\arctan(x)-\frac{π}{4}
(\partial)/(\partial x)((x^2)/(1+y^2))	\frac{\partial\:}{\partial\:x}(\frac{x^{2}}{1+y^{2}})
limit as x approaches 35 of (x^2)/5-7/x	\lim\:_{x\to\:35}(\frac{x^{2}}{5}-\frac{7}{x})
derivative of-x^2-4x-2	\frac{d}{dx}(-x^{2}-4x-2)
derivative of (x^2+1/x)	\frac{d}{dx}(\frac{x^{2}+1}{x})
derivative of 1/(ln^2(cos(sqrt(3x))))	\frac{d}{dx}(\frac{1}{\ln^{2}(\cos(\sqrt{3x}))})
sum from n=1 to infinity of (-5)^n	\sum\:_{n=1}^{\infty\:}(-5)^{n}
integral of cosh(0)	\int\:\cosh(0)
integral of (3cos(2θ))	\int\:(3\cos(2θ))dθ
integral of x/((y^2+x^2)^{3/2)}	\int\:\frac{x}{(y^{2}+x^{2})^{\frac{3}{2}}}dx
area x^2,-x+5,0	area\:x^{2},-x+5,0
derivative of (8x^3-2x+9)/x	derivative\:\frac{8x^{3}-2x+9}{x}
(\partial)/(\partial u)(u/(u+v))	\frac{\partial\:}{\partial\:u}(\frac{u}{u+v})
derivative of (x-2)(3x+3)	derivative\:(x-2)(3x+3)

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