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Popular Calculus Problems

(\partial)/(\partial x)(ln(1/(2+3e^x)))	\frac{\partial\:}{\partial\:x}(\ln(\frac{1}{2+3e^{x}}))
limit as x approaches 1 of (3x-2)/(x-1)	\lim\:_{x\to\:1}(\frac{3x-2}{x-1})
join 1/3 tan^3(x)-tan(x)+x	join\:\frac{1}{3}\tan^{3}(x)-\tan(x)+x
limit as x approaches-8 of (x+2)/(x+8)	\lim\:_{x\to\:-8}(\frac{x+2}{x+8})
limit as x approaches 2 of 2x^2+7x-1	\lim\:_{x\to\:2}(2x^{2}+7x-1)
limit as x approaches-3+of 2x^2-6	\lim\:_{x\to\:-3+}(2x^{2}-6)
(\partial)/(\partial x)(x^m)	\frac{\partial\:}{\partial\:x}(x^{m})
(\partial)/(\partial x)(((5x+3))/((y-2)))	\frac{\partial\:}{\partial\:x}(\frac{(5x+3)}{(y-2)})
limit as x approaches 5 of (2^x-32)/(x-5)	\lim\:_{x\to\:5}(\frac{2^{x}-32}{x-5})
(\partial)/(\partial t)(te^{s/t})	\frac{\partial\:}{\partial\:t}(te^{\frac{s}{t}})
derivative of (t+7)^2	derivative\:(t+7)^{2}
limit as x approaches infinity of x+0	\lim\:_{x\to\:\infty\:}(x+0)
taylor e^{x+1}	taylor\:e^{x+1}
derivative of arctan(sqrt((1+x/(1-x))))	\frac{d}{dx}(\arctan(\sqrt{\frac{1+x}{1-x}}))
d/(dt)(te^{-1})	\frac{d}{dt}(te^{-1})
(cos(x)-xsin(x))^'	(\cos(x)-x\sin(x))^{\prime\:}
derivative of y=ln((x^4-10)/x)	derivative\:y=\ln(\frac{x^{4}-10}{x})
derivative of x^3-3	derivative\:x^{3}-3
integral of 5x^5	\int\:5x^{5}dx
derivative of (1+cos^2(x))^5	derivative\:(1+\cos^{2}(x))^{5}
sum from n=0 to infinity of ((e^n))/5	\sum\:_{n=0}^{\infty\:}\frac{(e^{n})}{5}
derivative of-8x^3	\frac{d}{dx}(-8x^{3})
integral from 1/7 to 5 of 6xln(7x)	\int\:_{\frac{1}{7}}^{5}6x\ln(7x)dx
derivative of 8/(x-3)	\frac{d}{dx}(\frac{8}{x-3})
limit as x approaches pi/2 of x*sec(x)	\lim\:_{x\to\:\frac{π}{2}}(x\cdot\:\sec(x))
xy^'+2y=0	xy^{\prime\:}+2y=0
integral from 0 to a of r^2e^{-(2r)/a}	\int\:_{0}^{a}r^{2}e^{-\frac{2r}{a}}dr
integral of (2x^2)/(2x-3)	\int\:\frac{2x^{2}}{2x-3}dx
derivative of-(2x(-x^2+3)/((x^2+1)^3))	\frac{d}{dx}(-\frac{2x(-x^{2}+3)}{(x^{2}+1)^{3}})
(\partial)/(\partial x)((sqrt(x)+sqrt(y))^2)	\frac{\partial\:}{\partial\:x}((\sqrt{x}+\sqrt{y})^{2})
integral of 2(2x+8)^4	\int\:2(2x+8)^{4}dx
integral from 0 to sqrt(pi of)4xcos(x^2)	\int\:_{0}^{\sqrt{π}}4x\cos(x^{2})dx
(dx)/(dt)=x-1	\frac{dx}{dt}=x-1
integral of 1/((1+x)^4)	\int\:\frac{1}{(1+x)^{4}}dx
limit as x approaches pi/2 of cot(x)	\lim\:_{x\to\:\frac{π}{2}}(\cot(x))
sum from n=5 to infinity of 1/(2^n)	\sum\:_{n=5}^{\infty\:}\frac{1}{2^{n}}
derivative of 7x^2ln(x)	\frac{d}{dx}(7x^{2}\ln(x))
derivative of x^3+y^3-3x^2y^2+1	derivative\:x^{3}+y^{3}-3x^{2}y^{2}+1
y^{''}+y^'-2y=2t	y^{\prime\:\prime\:}+y^{\prime\:}-2y=2t
integral from 0 to 3 of x^2	\int\:_{0}^{3}x^{2}dx
integral of (2x^3+x^2-x)/(x^2)	\int\:\frac{2x^{3}+x^{2}-x}{x^{2}}dx
integral of (e^x+x^e)	\int\:(e^{x}+x^{e})dx
f(x)=-arctan(x)	f(x)=-\arctan(x)
simplify x5^{2x}	simplify\:x5^{2x}
derivative of 1/(sqrt(1-sin^2(x)))	\frac{d}{dx}(\frac{1}{\sqrt{1-\sin^{2}(x)}})
integral of 7/(1-x^2)	\int\:\frac{7}{1-x^{2}}dx
derivative of (2t-1)(5t-5)^{-1}	derivative\:(2t-1)(5t-5)^{-1}
limit as x approaches 2 of 1/((x-2)^3)	\lim\:_{x\to\:2}(\frac{1}{(x-2)^{3}})
y^{''}-y^'-2y=-2t+8t^2	y^{\prime\:\prime\:}-y^{\prime\:}-2y=-2t+8t^{2}
inverse oflaplace 4/((s-1)^3)	inverselaplace\:\frac{4}{(s-1)^{3}}
y^'=a-by^2	y^{\prime\:}=a-by^{2}
(\partial)/(\partial x)(cos(4x))	\frac{\partial\:}{\partial\:x}(\cos(4x))
(\partial)/(\partial y)(e^x+z^2)	\frac{\partial\:}{\partial\:y}(e^{x}+z^{2})
derivative of f(x)= 1/(sqrt(x+4))	derivative\:f(x)=\frac{1}{\sqrt{x+4}}
integral of e^x+2cos(x)-3/(cos^2(x))	\int\:e^{x}+2\cos(x)-\frac{3}{\cos^{2}(x)}dx
(\partial)/(\partial y)((3y)/(x^2+y^2))	\frac{\partial\:}{\partial\:y}(\frac{3y}{x^{2}+y^{2}})
limit as x approaches 0 of (cos(x))/(x-pi/2)	\lim\:_{x\to\:0}(\frac{\cos(x)}{x-\frac{π}{2}})
integral of (2x^2)/(1-6x^3)	\int\:\frac{2x^{2}}{1-6x^{3}}dx
(\partial)/(\partial x)(sin(y)-ysin(x))	\frac{\partial\:}{\partial\:x}(\sin(y)-y\sin(x))
tangent of f(x)=3x^3-x^2+2,(1,4)	tangent\:f(x)=3x^{3}-x^{2}+2,(1,4)
integral of t^3*ln(t^2)	\int\:t^{3}\cdot\:\ln(t^{2})dt
(\partial)/(\partial y)(xy^3-x^2)	\frac{\partial\:}{\partial\:y}(xy^{3}-x^{2})
(\partial)/(\partial y)(xe^{-x^2y})	\frac{\partial\:}{\partial\:y}(xe^{-x^{2}y})
integral of (5x^4)/(x^5-3)	\int\:\frac{5x^{4}}{x^{5}-3}dx
sum from n=1 to infinity of 1/(2n)	\sum\:_{n=1}^{\infty\:}\frac{1}{2n}
area y=x^2-4,y=-2x	area\:y=x^{2}-4,y=-2x
derivative of e^{(x^3/3})	\frac{d}{dx}(e^{\frac{x^{3}}{3}})
integral of (tan^3(8/z))/(z^2)	\int\:\frac{\tan^{3}(\frac{8}{z})}{z^{2}}dz
integral of (x^2)/(x^2-4)	\int\:\frac{x^{2}}{x^{2}-4}dx
integral of sqrt(x)(6+10x)	\int\:\sqrt{x}(6+10x)dx
integral of 13sec^{-2}(xta)n^3x	\int\:13\sec^{-2}(xta)n^{3}xdx
y^{''}+y^'+y=0.5	y^{\prime\:\prime\:}+y^{\prime\:}+y=0.5
f^'(x)=5	f^{\prime\:}(x)=5
derivative of ((e^x)/(ln(x)))	\frac{d}{dx}(\frac{(e^{x})}{\ln(x)})
tangent of cos(x),\at x= pi/2	tangent\:\cos(x),\at\:x=\frac{π}{2}
d/(d{r)}({r}sqrt(1-{r)^2})	\frac{d}{d{r}}({r}\sqrt{1-{r}^{2}})
limit as x approaches infinity of 2x-1	\lim\:_{x\to\:\infty\:}(2x-1)
y^'=y(1-y),y(0)=-2	y^{\prime\:}=y(1-y),y(0)=-2
integral of (y+1)/(y^2+y+1)	\int\:\frac{y+1}{y^{2}+y+1}dy
(\partial)/(\partial z)(xcos(y)sin(z))	\frac{\partial\:}{\partial\:z}(x\cos(y)\sin(z))
integral of (x^3)/(sqrt(x-1))	\int\:\frac{x^{3}}{\sqrt{x-1}}dx
limit as x approaches 2 of (x+6)/(x-2)	\lim\:_{x\to\:2}(\frac{x+6}{x-2})
integral of 3x^2sqrt((2x^3+5))	\int\:3x^{2}\sqrt{(2x^{3}+5)}dx
(dy)/(dx)=-ky	\frac{dy}{dx}=-ky
limit as x approaches 3 of \|x+1\|+\|x-1\|	\lim\:_{x\to\:3}(\left\|x+1\right\|+\left\|x-1\right\|)
derivative of arcsec(5x)	derivative\:\arcsec(5x)
(\partial}{\partial L}(L^{1/4)/K ^{1/4})	\frac{\partial\:}{\partial\:L}(L^{\frac{1}{4}}{K}^{\frac{1}{4}})
(\partial)/(\partial x)((4xy-5)^2)	\frac{\partial\:}{\partial\:x}((4xy-5)^{2})
area e^{(x/4)},x=4,y=1	area\:e^{(\frac{x}{4})},x=4,y=1
d/(dt)(-4sin(t))	\frac{d}{dt}(-4\sin(t))
integral of ((x^3))/(x^2-81)	\int\:\frac{(x^{3})}{x^{2}-81}dx
area x^2,-1<= x<= 2	area\:x^{2},-1\le\:x\le\:2
integral of (-5)/(6x)	\int\:\frac{-5}{6x}dx
integral of x^2(x^3+1)	\int\:x^{2}(x^{3}+1)dx
integral of 1/(x(3x+1)^2)	\int\:\frac{1}{x(3x+1)^{2}}dx
derivative of 6e^x(cos(x-sin(x)))	\frac{d}{dx}(6e^{x}(\cos(x)-\sin(x)))
integral of 8t^3	\int\:8t^{3}dt
derivative of sqrt(1/x)	\frac{d}{dx}(\sqrt{\frac{1}{x}})
limit as x approaches 1+of (x^2)/(\|1-x\|)	\lim\:_{x\to\:1+}(\frac{x^{2}}{\left\|1-x\right\|})
integral from 0 to pi of cos(θ)	\int\:_{0}^{π}\cos(θ)dθ

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