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Popular Calculus Problems

slope of h=(xx^2+2),(x+h,(x+h)^2+2)	slope\:h=(xx^{2}+2),(x+h,(x+h)^{2}+2)
integral of (2x)/(sqrt(x^2-27))	\int\:\frac{2x}{\sqrt{x^{2}-27}}dx
integral of 3/2 x	\int\:\frac{3}{2}xdx
y^'=ysin(4x)	y^{\prime\:}=y\sin(4x)
d/(dy)(2xsin(y))	\frac{d}{dy}(2x\sin(y))
(\partial)/(\partial x)(-(x-4)^2-(y-1)^2)	\frac{\partial\:}{\partial\:x}(-(x-4)^{2}-(y-1)^{2})
integral of 1/(sqrt(x))	\int\:\frac{1}{\sqrt{x}}dx
integral of 1/(81+16x^2)	\int\:\frac{1}{81+16x^{2}}dx
y^'+y=sin(2t)	y^{\prime\:}+y=\sin(2t)
(\partial)/(\partial y)(xy+yz)	\frac{\partial\:}{\partial\:y}(xy+yz)
limit as x approaches-1-of (-1)/(x^2-1)	\lim\:_{x\to\:-1-}(\frac{-1}{x^{2}-1})
taylor sqrt(1+x^3)	taylor\:\sqrt{1+x^{3}}
derivative of e^{{r}(xx})	\frac{d}{dx}(e^{{r}(x)x})
d/(dy)(sin(x)cos(y))	\frac{d}{dy}(\sin(x)\cos(y))
tangent of f(x)=e^{-x^2},\at x=5	tangent\:f(x)=e^{-x^{2}},\at\:x=5
limit as x approaches 0 of-3/(1-3x)	\lim\:_{x\to\:0}(-\frac{3}{1-3x})
derivative of f(x)=cot^2(sin(θ))	derivative\:f(x)=\cot^{2}(\sin(θ))
derivative of sec(xy)	\frac{d}{dx}(\sec(x)y)
(dy)/(dt)=y-5	\frac{dy}{dt}=y-5
integral of (5x^2+4)^3	\int\:(5x^{2}+4)^{3}dx
limit as x approaches-2 of 3-4x	\lim\:_{x\to\:-2}(3-4x)
limit as (x,y) approaches (0,0) of v/u	\lim\:_{(x,y)\to\:(0,0)}(\frac{v}{u})
y^{''}-y^'+y=2sin(3x)	y^{\prime\:\prime\:}-y^{\prime\:}+y=2\sin(3x)
derivative of (-xsin(x)-cos(x))/(6x^2)	derivative\:\frac{-x\sin(x)-\cos(x)}{6x^{2}}
(dy)/(dx)=xe^x	\frac{dy}{dx}=xe^{x}
tangent of f(x)=-3x^2-4x-2,\at x=2	tangent\:f(x)=-3x^{2}-4x-2,\at\:x=2
integral of xsqrt(x+1)	\int\:x\sqrt{x+1}dx
integral from 0 to 1 of 4cos((pit)/2)	\int\:_{0}^{1}4\cos(\frac{πt}{2})dt
integral of 2e^{3x}sin(2x)	\int\:2e^{3x}\sin(2x)dx
integral from 0 to 7r of sqrt(49r^2-y^2)	\int\:_{0}^{7r}\sqrt{49r^{2}-y^{2}}dy
integral of ln(1+r^2)r	\int\:\ln(1+r^{2})rdr
(\partial)/(\partial x)(yzln(xy))	\frac{\partial\:}{\partial\:x}(yz\ln(xy))
y(x+y+1)dx+(x+2y)dy=0	y(x+y+1)dx+(x+2y)dy=0
x^{''}-2x-5=0,x(0)=1,x(1)=3	x^{\prime\:\prime\:}-2x-5=0,x(0)=1,x(1)=3
integral of (39)/((1-x^2)^{3/2)}	\int\:\frac{39}{(1-x^{2})^{\frac{3}{2}}}dx
derivative of 5x(1-x/5)^2	derivative\:5x(1-\frac{x}{5})^{2}
limit as x approaches 2 of 2x-3	\lim\:_{x\to\:2}(2x-3)
integral of 6z	\int\:6zdz
(y^2)/x (dy)/(dx)-(sqrt(y^3+1))e^{3x}=0	\frac{y^{2}}{x}\frac{dy}{dx}-(\sqrt{y^{3}+1})e^{3x}=0
derivative of (x-1sqrt(x^2-2x+2))	\frac{d}{dx}((x-1)\sqrt{x^{2}-2x+2})
limit as x approaches-8 of ln(x+8)	\lim\:_{x\to\:-8}(\ln(x+8))
derivative of sqrt(x^2-9x+25)	\frac{d}{dx}(\sqrt{x^{2}-9x+25})
y^'=-(3y)/t-2-t^{-4}	y^{\prime\:}=-\frac{3y}{t}-2-t^{-4}
sum from n=0 to infinity of (e^n)/(3^n)	\sum\:_{n=0}^{\infty\:}\frac{e^{n}}{3^{n}}
integral from 1/3 to 1 of (y+4)/(y^2+2y)	\int\:_{\frac{1}{3}}^{1}\frac{y+4}{y^{2}+2y}dy
derivative of f(x)=\sqrt[9]{x}-9e^x	derivative\:f(x)=\sqrt[9]{x}-9e^{x}
limit as x approaches (3pi)/2 of ln(1+sin(x))	\lim\:_{x\to\:\frac{3π}{2}}(\ln(1+\sin(x)))
d/(dy)(sqrt(2x+3y))	\frac{d}{dy}(\sqrt{2x+3y})
integral from 4 to 8 of x/(x^2-1)	\int\:_{4}^{8}\frac{x}{x^{2}-1}dx
derivative of 3xe^{sqrt(x)}	\frac{d}{dx}(3xe^{\sqrt{x}})
derivative of y=e^{8x}cos(11x)	derivative\:y=e^{8x}\cos(11x)
derivative of f(x)=5(1-x^2)^9	derivative\:f(x)=5(1-x^{2})^{9}
integral of 1/((5x-3)(3-4x))	\int\:\frac{1}{(5x-3)(3-4x)}dx
(\partial)/(\partial x)((14x)/(7x^2+y^2+6))	\frac{\partial\:}{\partial\:x}(\frac{14x}{7x^{2}+y^{2}+6})
area y=2x,(-3,3)	area\:y=2x,(-3,3)
integral from 0 to pi/(32) of cos(8x)	\int\:_{0}^{\frac{π}{32}}\cos(8x)dx
derivative of ln(sqrt(2-x))	derivative\:\ln(\sqrt{2-x})
sum from n=0 to infinity of 6(-1/3)^n	\sum\:_{n=0}^{\infty\:}6(-\frac{1}{3})^{n}
(\partial)/(\partial x)(cos^6(x^4y^5))	\frac{\partial\:}{\partial\:x}(\cos^{6}(x^{4}y^{5}))
integral of sqrt(2+x^2)	\int\:\sqrt{2+x^{2}}dx
tangent of x^3-10x^2+12x+3	tangent\:x^{3}-10x^{2}+12x+3
integral of (3x^4)/2-4x^{3/2}	\int\:\frac{3x^{4}}{2}-4x^{\frac{3}{2}}dx
derivative of f(x)=(e^x+e^{-x})/2	derivative\:f(x)=\frac{e^{x}+e^{-x}}{2}
(dy)/(dx)=(5x+2y)/(5x+2y+2)	\frac{dy}{dx}=\frac{5x+2y}{5x+2y+2}
(d^2y)/(dx^2)=0	\frac{d^{2}y}{dx^{2}}=0
11x-4ysqrt(x^2+1)y^'=0,y(0)=3	11x-4y\sqrt{x^{2}+1}y^{\prime\:}=0,y(0)=3
(dy}{dx}=\frac{y+xcos^2(y/x))/x	\frac{dy}{dx}=\frac{y+x\cos^{2}(\frac{y}{x})}{x}
derivative of (0.9e^x/(tan(x)))	\frac{d}{dx}(\frac{0.9e^{x}}{\tan(x)})
limit as x approaches 2 of (4x+1)^{1/2}	\lim\:_{x\to\:2}((4x+1)^{\frac{1}{2}})
integral of (4x^2+5)/(0.4x^3+1.5x)	\int\:\frac{4x^{2}+5}{0.4x^{3}+1.5x}dx
(\partial)/(\partial x)(sin(x^2-3xy))	\frac{\partial\:}{\partial\:x}(\sin(x^{2}-3xy))
integral from 2 to 5 of 1/(x-3)	\int\:_{2}^{5}\frac{1}{x-3}dx
derivative of ((x^2+3x))/((2x+3)^3)	derivative\:\frac{(x^{2}+3x)}{(2x+3)^{3}}
integral of ln(x+x^2)	\int\:\ln(x+x^{2})dx
integral of x^2(7-x^3)^{2/3}	\int\:x^{2}(7-x^{3})^{\frac{2}{3}}dx
derivative of tan(x^2-4x)	\frac{d}{dx}(\tan(x^{2}-4x))
limit as x approaches-infinity of x^3-5x^2	\lim\:_{x\to\:-\infty\:}(x^{3}-5x^{2})
integral of x^2*sqrt(x-5)	\int\:x^{2}\cdot\:\sqrt{x-5}dx
derivative of y=x^2(x^3-1)^5	derivative\:y=x^{2}(x^{3}-1)^{5}
normal of y=sqrt(2x+1),\at x=4	normal\:y=\sqrt{2x+1},\at\:x=4
tangent of (x-y-1)^3=x	tangent\:(x-y-1)^{3}=x
sum from n=1 to infinity of (x^n)/(3^n)	\sum\:_{n=1}^{\infty\:}\frac{x^{n}}{3^{n}}
derivative of (x^2-x-2/(x^2-6x+9))	\frac{d}{dx}(\frac{x^{2}-x-2}{x^{2}-6x+9})
limit as x approaches 1 of (x+1)/(x+2)	\lim\:_{x\to\:1}(\frac{x+1}{x+2})
f^'(x)=x^4-3x^3-6x^2+6x-1	f^{\prime\:}(x)=x^{4}-3x^{3}-6x^{2}+6x-1
integral from 1 to 3 of 5x^3ln(x)	\int\:_{1}^{3}5x^{3}\ln(x)dx
integral from 0 to 2 of 1/(sqrt(16-x^2))	\int\:_{0}^{2}\frac{1}{\sqrt{16-x^{2}}}dx
d/(dθ)(3sin(2θ))	\frac{d}{dθ}(3\sin(2θ))
sum from n=1 to infinity of cos(4n)	\sum\:_{n=1}^{\infty\:}\cos(4n)
derivative of ae^{ax}	\frac{d}{dx}(ae^{ax})
derivative of (x^3+2x-7(3+x-x^2))	\frac{d}{dx}((x^{3}+2x-7)(3+x-x^{2}))
derivative of (x+1/x ^{-1})	\frac{d}{dx}((x+\frac{1}{x})^{-1})
(dy)/(dx)-2xy=8x	\frac{dy}{dx}-2xy=8x
limit as x approaches 1-of \|x-1\|	\lim\:_{x\to\:1-}(\left\|x-1\right\|)
integral of (4x^3)/(e^{2x^2)}	\int\:\frac{4x^{3}}{e^{2x^{2}}}dx
derivative of 1/((x-2^2))	\frac{d}{dx}(\frac{1}{(x-2)^{2}})
tangent of f(x)=x^2+2x+1,\at x=-3	tangent\:f(x)=x^{2}+2x+1,\at\:x=-3
slope of (8-4)(89)	slope\:(8-4)(89)
derivative of x^2-sin(x)	\frac{d}{dx}(x^{2}-\sin(x))
tangent of x^2+y^2=169,(5,-12)	tangent\:x^{2}+y^{2}=169,(5,-12)

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