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Popular Calculus Problems

limit as x approaches 6 of-5x^2+6x+8	\lim\:_{x\to\:6}(-5x^{2}+6x+8)
integral of 5000(1-(100)/((x+10)^2))	\int\:5000(1-\frac{100}{(x+10)^{2}})dx
(\partial)/(\partial y)((9x^2)/(y^{1/3)})	\frac{\partial\:}{\partial\:y}(\frac{9x^{2}}{y^{\frac{1}{3}}})
derivative of x^4-2x^2+2	\frac{d}{dx}(x^{4}-2x^{2}+2)
derivative of f(x)=(x^2)/(1+8x)	derivative\:f(x)=\frac{x^{2}}{1+8x}
laplacetransform-5y	laplacetransform\:-5y
area 3(x^3-x),0	area\:3(x^{3}-x),0
tangent of f(x)=4x^2+12x+1,\at x=-2	tangent\:f(x)=4x^{2}+12x+1,\at\:x=-2
(d^2)/(dx^2)(sin(3x^2))	\frac{d^{2}}{dx^{2}}(\sin(3x^{2}))
derivative of x^{{r}(x})	\frac{d}{dx}(x^{{r}(x)})
derivative of 30	\frac{d}{dx}(30)
area-x^2+3x,x-3	area\:-x^{2}+3x,x-3
(dy)/(dx)=(((1+y)^2))/((1+x)^3)	\frac{dy}{dx}=\frac{((1+y)^{2})}{(1+x)^{3}}
integral of e^{-2x}cos(e^{-x})	\int\:e^{-2x}\cos(e^{-x})dx
d/(dy)((x+y)/(x-y))	\frac{d}{dy}(\frac{x+y}{x-y})
derivative of (e^{2x+1}/((x-1)^2))	\frac{d}{dx}(\frac{e^{2x+1}}{(x-1)^{2}})
integral of 1/2 sin(2x)	\int\:\frac{1}{2}\sin(2x)dx
laplacetransform F(t)=2+4e^{-4t}-3e^{3t}	laplacetransform\:F(t)=2+4e^{-4t}-3e^{3t}
(\partial)/(\partial x)(ln(x+y/(2x)))	\frac{\partial\:}{\partial\:x}(\ln(x+\frac{y}{2x}))
limit as x approaches infinity of (1+7/x)^{2x}	\lim\:_{x\to\:\infty\:}((1+\frac{7}{x})^{2x})
derivative of x^2+(2a^3/x)	\frac{d}{dx}(x^{2}+\frac{2a^{3}}{x})
limit as x approaches+3-of 3/(x^2-9)	\lim\:_{x\to\:+3-}(\frac{3}{x^{2}-9})
y^3-(14x+8)+3xy^2y^'=0	y^{3}-(14x+8)+3xy^{2}y^{\prime\:}=0
x^'=x	x^{\prime\:}=x
limit as x approaches 0+of sin(x)ln(x)	\lim\:_{x\to\:0+}(\sin(x)\ln(x))
tangent of f(x)=x^2-2,(-4,14)	tangent\:f(x)=x^{2}-2,(-4,14)
derivative of (2x-8/(4x-3))	\frac{d}{dx}(\frac{2x-8}{4x-3})
derivative of (cos(4x)/x)	\frac{d}{dx}(\frac{\cos(4x)}{x})
(\partial)/(\partial x)(sin(ye^{xy}))	\frac{\partial\:}{\partial\:x}(\sin(ye^{xy}))
integral of e^{yx}	\int\:e^{yx}dx
y^{''}+9y^'=0,y(0)=1	y^{\prime\:\prime\:}+9y^{\prime\:}=0,y(0)=1
derivative of f(x)=4(x-3)^{2/3}	derivative\:f(x)=4(x-3)^{\frac{2}{3}}
derivative of arctan(c/x)	\frac{d}{dx}(\arctan(\frac{c}{x}))
tangent of f(x)=(5x)/(x-2),\at x=3	tangent\:f(x)=\frac{5x}{x-2},\at\:x=3
derivative of 16e^{-2x}	\frac{d}{dx}(16e^{-2x})
sum from n=3 to infinity of 3/2*1/(4^n)	\sum\:_{n=3}^{\infty\:}\frac{3}{2}\cdot\:\frac{1}{4^{n}}
integral from 0 to 8 of f(x)	\int\:_{0}^{8}f(x)dx
(dx)/(dt)=(2t^2+x^2)/(tx)	\frac{dx}{dt}=\frac{2t^{2}+x^{2}}{tx}
(d^2)/(dx^2)(x^{1/2})	\frac{d^{2}}{dx^{2}}(x^{\frac{1}{2}})
(\partial)/(\partial s)(arctan(rs))	\frac{\partial\:}{\partial\:s}(\arctan(rs))
tangent of f(x)= 6/x ,\at x=-7	tangent\:f(x)=\frac{6}{x},\at\:x=-7
derivative of (x^3+4x+7)5+1/(x^2)	derivative\:(x^{3}+4x+7)5+\frac{1}{x^{2}}
limit as x approaches 7+of (x+6)/(x-7)	\lim\:_{x\to\:7+}(\frac{x+6}{x-7})
limit as x approaches 3 of (x-3)/(9-x^2)	\lim\:_{x\to\:3}(\frac{x-3}{9-x^{2}})
derivative of (x^3+2xe^x)	\frac{d}{dx}((x^{3}+2x)e^{x})
limit as x approaches 1000 of x^{4/3}	\lim\:_{x\to\:1000}(x^{\frac{4}{3}})
derivative of e^{x^x}	derivative\:e^{x^{x}}
integral from-1 to 1 of (x^2-1/3)^2	\int\:_{-1}^{1}(x^{2}-\frac{1}{3})^{2}dx
integral of (5x^2)/((3+x^3)^2)	\int\:\frac{5x^{2}}{(3+x^{3})^{2}}dx
integral of (sqrt(x^3)+1/(sqrt(x)))	\int\:(\sqrt{x^{3}}+\frac{1}{\sqrt{x}})dx
(\partial)/(\partial y)(((x-y))/((x+y)))	\frac{\partial\:}{\partial\:y}(\frac{(x-y)}{(x+y)})
integral of 4xln(5x)	\int\:4x\ln(5x)dx
y^'=4y^2+xy^2,y(0)=1	y^{\prime\:}=4y^{2}+xy^{2},y(0)=1
derivative of (sin(3x)/(7x))	\frac{d}{dx}(\frac{\sin(3x)}{7x})
derivative of 1/(x^2-1/x)	\frac{d}{dx}(\frac{1}{x^{2}}-\frac{1}{x})
derivative of \sqrt[3]{x^2-4}	\frac{d}{dx}(\sqrt[3]{x^{2}-4})
integral of sec^6(4x)tan(4x)	\int\:\sec^{6}(4x)\tan(4x)dx
derivative of csc^2(x-1)	\frac{d}{dx}(\csc^{2}(x)-1)
area f(x)=x^2,0,4	area\:f(x)=x^{2},0,4
y^{''}-5y^'+6y=0,y(1)=e^2,y^'(1)=3e^2	y^{\prime\:\prime\:}-5y^{\prime\:}+6y=0,y(1)=e^{2},y^{\prime\:}(1)=3e^{2}
integral of x^2cos(x^3+5)	\int\:x^{2}\cos(x^{3}+5)dx
integral of (x^3)/(1+x^8)	\int\:\frac{x^{3}}{1+x^{8}}dx
derivative of 1/4 e^{-x/2}	\frac{d}{dx}(\frac{1}{4}e^{-\frac{x}{2}})
limit as x approaches pi of sin(x-pi)	\lim\:_{x\to\:π}(\sin(x-π))
limit as x approaches 0+of-3/x	\lim\:_{x\to\:0+}(-\frac{3}{x})
y^'=(4x^2+y^2)/(xy)	y^{\prime\:}=\frac{4x^{2}+y^{2}}{xy}
derivative of 5sqrt(x^3)	\frac{d}{dx}(5\sqrt{x^{3}})
y^'=(x^{10})/y	y^{\prime\:}=\frac{x^{10}}{y}
(\partial)/(\partial x)(3x+y)	\frac{\partial\:}{\partial\:x}(3x+y)
integral of (-2x^{-1})	\int\:(-2x^{-1})dx
laplacetransform cos(2*t)	laplacetransform\:\cos(2\cdot\:t)
(dy)/(dx)=(x-3)e^{-2y},y(3)=ln(3)	\frac{dy}{dx}=(x-3)e^{-2y},y(3)=\ln(3)
derivative of y=log_{2}(log_{2}(x))	derivative\:y=\log_{2}(\log_{2}(x))
limit as x approaches 1 of-(x^2)/2+2x+4	\lim\:_{x\to\:1}(-\frac{x^{2}}{2}+2x+4)
derivative of (x^3/3-10x^2+100x)	\frac{d}{dx}(\frac{x^{3}}{3}-10x^{2}+100x)
(1-xy)dx+(xy-x^2)dy=0	(1-xy)dx+(xy-x^{2})dy=0
integral of tan^2(x)x	\int\:\tan^{2}(x)xdx
derivative of 5tan^2(9x)	derivative\:5\tan^{2}(9x)
(\partial)/(\partial x)(-y^2sin(z))	\frac{\partial\:}{\partial\:x}(-y^{2}\sin(z))
integral from 3 to sqrt(11 of)x	\int\:_{3}^{\sqrt{11}}xdx
sum from n=1 to infinity of (4/7)^n	\sum\:_{n=1}^{\infty\:}(\frac{4}{7})^{n}
sum from n=0 to infinity of n!	\sum\:_{n=0}^{\infty\:}n!
(\partial)/(\partial x)(x/(x+2))	\frac{\partial\:}{\partial\:x}(\frac{x}{x+2})
(dy)/(dx)=5xe^{4y}	\frac{dy}{dx}=5xe^{4y}
limit as x approaches 2-of 5/(x-2)	\lim\:_{x\to\:2-}(\frac{5}{x-2})
integral of e^{2x}*sin(-3x)	\int\:e^{2x}\cdot\:\sin(-3x)dx
integral of (sqrt(3x)-2/(sqrt(x)))	\int\:(\sqrt{3x}-\frac{2}{\sqrt{x}})dx
integral of sin^2(x)*cos^5(x)	\int\:\sin^{2}(x)\cdot\:\cos^{5}(x)dx
tangent of f(x)=x^2-3,\at x=2	tangent\:f(x)=x^{2}-3,\at\:x=2
sum from n=2 to infinity of 2/(5^n)	\sum\:_{n=2}^{\infty\:}\frac{2}{5^{n}}
integral from-6 to-1 of 2x^{1/3}	\int\:_{-6}^{-1}2x^{\frac{1}{3}}dx
integral of (5+14x)/(49+25x^2)	\int\:\frac{5+14x}{49+25x^{2}}dx
limit as x approaches 0 of tan(e^x-1)	\lim\:_{x\to\:0}(\tan(e^{x}-1))
y^'-4y=e^{-4t}	y^{\prime\:}-4y=e^{-4t}
(\partial}{\partial t}(\frac{s-r)/t)	\frac{\partial\:}{\partial\:t}(\frac{s-r}{t})
(dy)/(dx)=sqrt(5y)e^{x+4}	\frac{dy}{dx}=\sqrt{5y}e^{x+4}
integral of ((-x^2))/(sqrt(8x-x^2))	\int\:\frac{(-x^{2})}{\sqrt{8x-x^{2}}}dx
(e^{2t})^'	(e^{2t})^{\prime\:}
integral of sin(θ)cos(θ)	\int\:\sin(θ)\cos(θ)dθ
integral from-2 to 3 of 1/(x^4)	\int\:_{-2}^{3}\frac{1}{x^{4}}dx

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