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Popular Calculus Problems

derivative of cos(x/2)	derivative\:\cos(\frac{x}{2})
limit as x approaches 4 of (x^2-8)/(x^4)	\lim\:_{x\to\:4}(\frac{x^{2}-8}{x^{4}})
integral of xln(ln(x))	\int\:x\ln(\ln(x))dx
limit as x approaches 0 of (1-x/3)^{1/x}	\lim\:_{x\to\:0}((1-\frac{x}{3})^{\frac{1}{x}})
derivative of arctan(-2x)	derivative\:\arctan(-2x)
y^{''}+by^'=0	y^{\prime\:\prime\:}+by^{\prime\:}=0
area x^2,x^2-4x+4,0,2	area\:x^{2},x^{2}-4x+4,0,2
integral of 2-1/x	\int\:2-\frac{1}{x}dx
(\partial)/(\partial x)(2cos(xy^2))	\frac{\partial\:}{\partial\:x}(2\cos(xy^{2}))
derivative of ((4x^2+8x+6))/(sqrt(x))	derivative\:\frac{(4x^{2}+8x+6)}{\sqrt{x}}
limit as x approaches 0 of \|x-4\|	\lim\:_{x\to\:0}(\left\|x-4\right\|)
integral from-3 to 1 of (x^2-4x)	\int\:_{-3}^{1}(x^{2}-4x)dx
derivative of ln(ln(x^2+1))	\frac{d}{dx}(\ln(\ln(x^{2}+1)))
y^{''}+a^2y=0	y^{\prime\:\prime\:}+a^{2}y=0
xy^{''}+3y^'=0	xy^{\prime\:\prime\:}+3y^{\prime\:}=0
(\partial)/(\partial x)(ln(x^2-y))	\frac{\partial\:}{\partial\:x}(\ln(x^{2}-y))
d/(dy)((y^3)/8)	\frac{d}{dy}(\frac{y^{3}}{8})
d/(dt)(sin(2pit))	\frac{d}{dt}(\sin(2πt))
tangent of y=x^4+8x^2-x,(1,8)	tangent\:y=x^{4}+8x^{2}-x,(1,8)
integral of sqrt(x+2)-1/(x+1)	\int\:\sqrt{x+2}-\frac{1}{x+1}dx
integral of (x+1)/(x^2+2x)	\int\:\frac{x+1}{x^{2}+2x}dx
sum from n=1 to infinity of 1/3 (e/2)^n	\sum\:_{n=1}^{\infty\:}\frac{1}{3}(\frac{e}{2})^{n}
integral of (x^5+2x^3-3x)/((x^2+1)^3)	\int\:\frac{x^{5}+2x^{3}-3x}{(x^{2}+1)^{3}}dx
integral of 2e^{y^2}	\int\:2e^{y^{2}}dy
derivative of e^{2x^x}	derivative\:e^{2x^{x}}
integral from 1 to 4 of (x+sqrt(x))	\int\:_{1}^{4}(x+\sqrt{x})dx
integral of ((x^4+81))/(x(x^2+9)^2)	\int\:\frac{(x^{4}+81)}{x(x^{2}+9)^{2}}dx
inverse oflaplace 1/(s^2-16)	inverselaplace\:\frac{1}{s^{2}-16}
integral from-infinity to 0 of e^{-x^2}	\int\:_{-\infty\:}^{0}e^{-x^{2}}dx
integral of x*ln^4(x)	\int\:x\cdot\:\ln^{4}(x)dx
limit as x approaches 2-of-1/(x-2)	\lim\:_{x\to\:2-}(-\frac{1}{x-2})
derivative of-4cos(x/2)	\frac{d}{dx}(-4\cos(\frac{x}{2}))
y^{''}-y^'-30y=0	y^{\prime\:\prime\:}-y^{\prime\:}-30y=0
inverse oflaplace (16)/(s^2+9)	inverselaplace\:\frac{16}{s^{2}+9}
(\partial}{\partial y}(\frac{4x)/y)	\frac{\partial\:}{\partial\:y}(\frac{4x}{y})
derivative of-1/2 x^4	\frac{d}{dx}(-\frac{1}{2}x^{4})
limit as x approaches 4 of 3x^3	\lim\:_{x\to\:4}(3x^{3})
integral of x^2cos(1/4 x)	\int\:x^{2}\cos(\frac{1}{4}x)dx
slope of (16,1.2),(32,2.4)	slope\:(16,1.2),(32,2.4)
sum from n=2 to infinity of 3/(n(n+2))	\sum\:_{n=2}^{\infty\:}\frac{3}{n(n+2)}
implicit (dy)/(dx),y=2x^2+5yx	implicit\:\frac{dy}{dx},y=2x^{2}+5yx
integral of x^2*arctan(x)	\int\:x^{2}\cdot\:\arctan(x)dx
integral from 1 to x of t^2	\int\:_{1}^{x}t^{2}dt
slope of xy-8y^2=4,(18,2)	slope\:xy-8y^{2}=4,(18,2)
laplacetransform 5+2tcos(2t)	laplacetransform\:5+2t\cos(2t)
derivative of f(x)=2^{2^x}	derivative\:f(x)=2^{2^{x}}
integral from 1 to 6 of 4/x	\int\:_{1}^{6}\frac{4}{x}dx
integral of sqrt(2x+6)	\int\:\sqrt{2x+6}dx
area 1/(4(1+x^2)), 1/8 x^2	area\:\frac{1}{4(1+x^{2})},\frac{1}{8}x^{2}
sum from n=0 to infinity of e^{-8n}	\sum\:_{n=0}^{\infty\:}e^{-8n}
derivative of (1-x)^3-log_{e}(1-x)	derivative\:(1-x)^{3}-\log_{e}(1-x)
derivative of (5x^2)/(3x-1)	derivative\:\frac{5x^{2}}{3x-1}
integral from 1 to 2 of 3-6/(x^2)	\int\:_{1}^{2}3-\frac{6}{x^{2}}dx
integral of (6cosh(sqrt(x)))/(sqrt(x))	\int\:\frac{6\cosh(\sqrt{x})}{\sqrt{x}}dx
y^{'''}+4y^{''}-16y^'-64y=0	y^{\prime\:\prime\:\prime\:}+4y^{\prime\:\prime\:}-16y^{\prime\:}-64y=0
derivative of 5cos(x-cos(5x))	\frac{d}{dx}(5\cos(x)-\cos(5x))
integral of (3x^2-x+1)/(x^3-x^2)	\int\:\frac{3x^{2}-x+1}{x^{3}-x^{2}}dx
y^{''}+49y=cos(10t)	y^{\prime\:\prime\:}+49y=\cos(10t)
derivative of ln(x^3+5x+3)	derivative\:\ln(x^{3}+5x+3)
limit as x approaches 1 of xsin(1/x)	\lim\:_{x\to\:1}(x\sin(\frac{1}{x}))
tangent of y=x^4-3x^2+2,(1,0)	tangent\:y=x^{4}-3x^{2}+2,(1,0)
limit as x approaches 2-of (\|x-x\|)/(x-2)	\lim\:_{x\to\:2-}(\frac{\left\|x-x\right\|}{x-2})
derivative of tan(3xsc^3x)	\frac{d}{dx}(\tan(3x)sc^{3}x)
integral of 1/(xsqrt(1-4x^2))	\int\:\frac{1}{x\sqrt{1-4x^{2}}}dx
derivative of f(x)=(x^4)/4-2x^2-4	derivative\:f(x)=\frac{x^{4}}{4}-2x^{2}-4
derivative of x^2-2x+4	derivative\:x^{2}-2x+4
derivative of f(x)=4x^{5/4}+6x^{3/2}+3x	derivative\:f(x)=4x^{\frac{5}{4}}+6x^{\frac{3}{2}}+3x
y^{''}+12y^'+36y=0,y(1)=0,y^'(1)=1	y^{\prime\:\prime\:}+12y^{\prime\:}+36y=0,y(1)=0,y^{\prime\:}(1)=1
derivative of 2^{60}	derivative\:2^{60}
y^'=(2xy-y^4)/(3x^2)	y^{\prime\:}=\frac{2xy-y^{4}}{3x^{2}}
derivative of f(x)=sqrt(x)(x-10)	derivative\:f(x)=\sqrt{x}(x-10)
5y^{''}+32y=0,y(0)=8,y^'(0)=5	5y^{\prime\:\prime\:}+32y=0,y(0)=8,y^{\prime\:}(0)=5
integral of 1/2 xcos(x^2)	\int\:\frac{1}{2}x\cos(x^{2})dx
integral of 3/(x^3)	\int\:\frac{3}{x^{3}}dx
laplacetransform f(t)=cos(5t)+sin(2t)	laplacetransform\:f(t)=\cos(5t)+\sin(2t)
y^{''}-y=0,y(0)=6	y^{\prime\:\prime\:}-y=0,y(0)=6
integral of x/((sqrt(1+x^2)))	\int\:\frac{x}{(\sqrt{1+x^{2}})}dx
limit as x approaches-1 of (x^3+1)/(x-1)	\lim\:_{x\to\:-1}(\frac{x^{3}+1}{x-1})
integral of (x^2)/((x^2+1))	\int\:\frac{x^{2}}{(x^{2}+1)}dx
laplacetransform 1-1e^{(-t-2)}	laplacetransform\:1-1e^{(-t-2)}
area 2x-x^2,x^2	area\:2x-x^{2},x^{2}
area x=2-y^2,x=y	area\:x=2-y^{2},x=y
y^{''}-4y=e^{2x}	y^{\prime\:\prime\:}-4y=e^{2x}
limit as x approaches 0 of sin(x^x)	\lim\:_{x\to\:0}(\sin(x^{x}))
integral of 1/(x^2+6x+58)	\int\:\frac{1}{x^{2}+6x+58}dx
derivative of f(t)=sin^2(e^{sin^2(t)})	derivative\:f(t)=\sin^{2}(e^{\sin^{2}(t)})
tangent of 2/(sqrt(x)),\at x= 1/4	tangent\:\frac{2}{\sqrt{x}},\at\:x=\frac{1}{4}
tangent of y=(-2x)/(x^2+1),(1,-1)	tangent\:y=\frac{-2x}{x^{2}+1},(1,-1)
limit as x approaches 5 of 3x^2-2x-7	\lim\:_{x\to\:5}(3x^{2}-2x-7)
tangent of f(x)=2x^2+5x-3,(1,4)	tangent\:f(x)=2x^{2}+5x-3,(1,4)
derivative of Axe^{-x}cos(2x+Bxe^{-x}sin(2x))	\frac{d}{dx}(Axe^{-x}\cos(2x)+Bxe^{-x}\sin(2x))
integral from-2 to 3 of 4/(x^4)	\int\:_{-2}^{3}\frac{4}{x^{4}}dx
derivative of 1/(x^2-x)	\frac{d}{dx}(\frac{1}{x^{2}-x})
integral of-2e^{x^2}sin(2y)+(x^2)/2+1	\int\:-2e^{x^{2}}\sin(2y)+\frac{x^{2}}{2}+1
taylor 4+x^2+4x^4,3	taylor\:4+x^{2}+4x^{4},3
integral of (7e^{3t})/(1+e^{6t)}	\int\:\frac{7e^{3t}}{1+e^{6t}}dt
area 2x^2+3,-1,2	area\:2x^{2}+3,-1,2
integral of x/(sqrt(x^2+36))	\int\:\frac{x}{\sqrt{x^{2}+36}}dx
derivative of e^{-kx^2}	\frac{d}{dx}(e^{-kx^{2}})
integral from 1 to infinity of 1/(3x-2)	\int\:_{1}^{\infty\:}\frac{1}{3x-2}dx

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