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Popular Calculus Problems

derivative of-(13e^{1/x}/(x^2))	\frac{d}{dx}(-\frac{13e^{\frac{1}{x}}}{x^{2}})
limit as x approaches 14 of sqrt(x^2-9)	\lim\:_{x\to\:14}(\sqrt{x^{2}-9})
area y= 1/x ,y=x	area\:y=\frac{1}{x},y=x
integral of 4x^2-x^4	\int\:4x^{2}-x^{4}dx
limit as x approaches-1+of x+2	\lim\:_{x\to\:-1+}(x+2)
(dx)/(dt)=8(x^2+1),x(pi/4)=1	\frac{dx}{dt}=8(x^{2}+1),x(\frac{π}{4})=1
derivative of (-1/((x-1)^2))	\frac{d}{dx}(\frac{-1}{(x-1)^{2}})
(dy)/(dt)-2ty=12t^2e^{t^2}	\frac{dy}{dt}-2ty=12t^{2}e^{t^{2}}
y^'=(2y^2)+xy^2	y^{\prime\:}=(2y^{2})+xy^{2}
f^'(x)=2x-3/(x^4)	f^{\prime\:}(x)=2x-\frac{3}{x^{4}}
tangent of f(x)= 2/(3x+1)	tangent\:f(x)=\frac{2}{3x+1}
integral from 0 to 1 of 7e^{-7sqrt(x)}	\int\:_{0}^{1}7e^{-7\sqrt{x}}dx
limit as x approaches 5 of (x+2)/(x-4)	\lim\:_{x\to\:5}(\frac{x+2}{x-4})
integral of 0.1t	\int\:0.1tdt
(\partial)/(\partial x)(x*ln(y))	\frac{\partial\:}{\partial\:x}(x\cdot\:\ln(y))
derivative of x^2+sqrt(x^2+1)	\frac{d}{dx}(x^{2}+\sqrt{x^{2}+1})
derivative of y=2e^{-4x^2}	derivative\:y=2e^{-4x^{2}}
limit as x approaches 0 of (8^x-5^x)/x	\lim\:_{x\to\:0}(\frac{8^{x}-5^{x}}{x})
integral of (x^3)/(x^2+3x+2)	\int\:\frac{x^{3}}{x^{2}+3x+2}dx
integral from 0 to pi/(42) of tan(14x)	\int\:_{0}^{\frac{π}{42}}\tan(14x)dx
integral of x/(\sqrt[4]{x+6)}	\int\:\frac{x}{\sqrt[4]{x+6}}dx
tangent of (x^2)/(x-10),\at x=11	tangent\:\frac{x^{2}}{x-10},\at\:x=11
derivative of f(x)=xe^{3x}	derivative\:f(x)=xe^{3x}
integral of cos((npix)/l)	\int\:\cos(\frac{nπx}{l})dx
limit as x approaches 1 of 4-x	\lim\:_{x\to\:1}(4-x)
integral of 4tan^3(x)	\int\:4\tan^{3}(x)dx
y^'+6/5 y=1-1/6 t	y^{\prime\:}+\frac{6}{5}y=1-\frac{1}{6}t
derivative of f(x)=(x^3-8)^{2/3}	derivative\:f(x)=(x^{3}-8)^{\frac{2}{3}}
y^{''}+81y=cos(8t)	y^{\prime\:\prime\:}+81y=\cos(8t)
derivative of e^3+2	derivative\:e^{3}+2
integral from 1 to 4 of 1/(x^2)-8/(x^3)	\int\:_{1}^{4}\frac{1}{x^{2}}-\frac{8}{x^{3}}dx
x^'=x^3	x^{\prime\:}=x^{3}
maclaurin 1/(1+cos^2(x))	maclaurin\:\frac{1}{1+\cos^{2}(x)}
integral of 4x^3+24x-1	\int\:4x^{3}+24x-1dx
limit as x approaches 3 of (3-\|x\|)/(x+3)	\lim\:_{x\to\:3}(\frac{3-\left\|x\right\|}{x+3})
y^{''}+2ky^'+ak^2y=0	y^{\prime\:\prime\:}+2ky^{\prime\:}+ak^{2}y=0
inverse oflaplace (s+3)/(s^2+4s+8)	inverselaplace\:\frac{s+3}{s^{2}+4s+8}
limit as x approaches-infinity of x/x	\lim\:_{x\to\:-\infty\:}(\frac{x}{x})
(\partial)/(\partial x)(-(2x)/((1+x^2)^2))	\frac{\partial\:}{\partial\:x}(-\frac{2x}{(1+x^{2})^{2}})
xy^'+2y=(sin(x))/x	xy^{\prime\:}+2y=\frac{\sin(x)}{x}
y^'=7xe^y	y^{\prime\:}=7xe^{y}
(1+x^2)y+xy^'+ax=0	(1+x^{2})y+xy^{\prime\:}+ax=0
limit as k approaches 0 of (x^2k+3xk^2+k^3)/(2xk+5k^2)	\lim\:_{k\to\:0}(\frac{x^{2}k+3xk^{2}+k^{3}}{2xk+5k^{2}})
derivative of (1+x/(1+e^x))	\frac{d}{dx}(\frac{1+x}{1+e^{x}})
x^2y^{''}+9xy^'+16y=0	x^{2}y^{\prime\:\prime\:}+9xy^{\prime\:}+16y=0
f(x)=sin(5x)	f(x)=\sin(5x)
limit as x approaches-3 of-x^2+6x-2	\lim\:_{x\to\:-3}(-x^{2}+6x-2)
integral of 54.0595e^{sqrt(x)}x	\int\:54.0595e^{\sqrt{x}}xdx
(\partial)/(\partial x)(in(x+y)/(x-y))	\frac{\partial\:}{\partial\:x}(in\frac{x+y}{x-y})
derivative of (x^2/((x+2i)^2))	\frac{d}{dx}(\frac{x^{2}}{(x+2i)^{2}})
v'=(8*9.8+3.1v^2)/8	v\prime\:=\frac{8\cdot\:9.8+3.1v^{2}}{8}
limit as x approaches 3 of (x^2+1)/(10)	\lim\:_{x\to\:3}(\frac{x^{2}+1}{10})
y^{''}-5y^'=8t	y^{\prime\:\prime\:}-5y^{\prime\:}=8t
y^'=y,y(0)=1	y^{\prime\:}=y,y(0)=1
integral of ((2x+1))/(sqrt(x^2-1))	\int\:\frac{(2x+1)}{\sqrt{x^{2}-1}}dx
derivative of 2e^x(cos(x)-sin(x))	derivative\:2e^{x}(\cos(x)-\sin(x))
integral from-2 to 3 of (x^3-x^2-6x)	\int\:_{-2}^{3}(x^{3}-x^{2}-6x)dx
d/(dt)(arcsin(t))	\frac{d}{dt}(\arcsin(t))
d/(dt)(cos(t)+sin(t))	\frac{d}{dt}(\cos(t)+\sin(t))
area y=x^2-19,y=18x	area\:y=x^{2}-19,y=18x
y^'+2y=2x	y^{\prime\:}+2y=2x
(\partial)/(\partial x)((x^2)/((x+y)^2))	\frac{\partial\:}{\partial\:x}(\frac{x^{2}}{(x+y)^{2}})
integral of tan^5(x/(14))	\int\:\tan^{5}(\frac{x}{14})dx
simplify sqrt(xy)	simplify\:\sqrt{xy}
derivative of (-2x-y)/(x+2y)	derivative\:\frac{-2x-y}{x+2y}
(d^4)/(dx^4)(sin(x^2))	\frac{d^{4}}{dx^{4}}(\sin(x^{2}))
integral of (x-1/x)^2*x	\int\:(x-\frac{1}{x})^{2}\cdot\:xdx
integral of (sinh(x))/(cosh(x))	\int\:\frac{\sinh(x)}{\cosh(x)}dx
derivative of e^{cosh(8x})	\frac{d}{dx}(e^{\cosh(8x)})
d/(dy)(4y)	\frac{d}{dy}(4y)
limit as x approaches 0 of 5/(x+1)+4x	\lim\:_{x\to\:0}(\frac{5}{x+1}+4x)
integral of (x^2+4x+8)/(x-2)	\int\:\frac{x^{2}+4x+8}{x-2}dx
derivative of-ln(x^2)	\frac{d}{dx}(-\ln(x^{2}))
derivative of x^4-8x^2+a	\frac{d}{dx}(x^{4}-8x^{2}+a)
integral of-x(\sqrt[3]{2x^2+4})	\int\:-x(\sqrt[3]{2x^{2}+4})dx
(\partial)/(\partial x)(e)	\frac{\partial\:}{\partial\:x}(e)
limit as x approaches-19+of k(x)	\lim\:_{x\to\:-19+}(k(x))
derivative of 4sin(pi*x)	derivative\:4\sin(π\cdot\:x)
integral from 0 to 1 of x^{-2}	\int\:_{0}^{1}x^{-2}dx
4(dy)/(dx)+36y=9	4\frac{dy}{dx}+36y=9
derivative of ((6x^2-11x+2))/((3x-1))	derivative\:\frac{(6x^{2}-11x+2)}{(3x-1)}
integral of (ln^2(x))	\int\:(\ln^{2}(x))dx
derivative of cos(y*(dy)/(dx))	\frac{d}{dx}(\cos(y)\cdot\:\frac{dy}{dx})
sum from n=2 to infinity of 1/((n-1)^2)	\sum\:_{n=2}^{\infty\:}\frac{1}{(n-1)^{2}}
maclaurin x/(e^x)	maclaurin\:\frac{x}{e^{x}}
(dy)/(dx)=e^{5x+6y}	\frac{dy}{dx}=e^{5x+6y}
taylor 1+e^{2x}	taylor\:1+e^{2x}
integral of sec^2(x)-5	\int\:\sec^{2}(x)-5dx
(dy)/(dt)=2*sqrt(y)	\frac{dy}{dt}=2\cdot\:\sqrt{y}
slope of x^2-5	slope\:x^{2}-5
limit as x approaches infinity of-3e^x	\lim\:_{x\to\:\infty\:}(-3e^{x})
derivative of-y/(y^2+x^2)	\frac{d}{dx}(-\frac{y}{y^{2}+x^{2}})
derivative of cos^4(x-2x^2)	\frac{d}{dx}(\cos^{4}(x)-2x^{2})
inverse oflaplace 1/(s+11)	inverselaplace\:\frac{1}{s+11}
(dy)/(dt)+ty=y	\frac{dy}{dt}+ty=y
slope ofintercept (-3,1),(2,-14)	slopeintercept\:(-3,1),(2,-14)
(\partial)/(\partial y)(2xy-sec^2(x))	\frac{\partial\:}{\partial\:y}(2xy-\sec^{2}(x))
simplify-2	simplify\:-2
tangent of 2x^2+x	tangent\:2x^{2}+x
integral of x^2-1/(x^2)	\int\:x^{2}-\frac{1}{x^{2}}dx

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