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Popular Calculus Problems

sum from n=0 to infinity of 7(-1/8)^n	\sum\:_{n=0}^{\infty\:}7(-\frac{1}{8})^{n}
xy^'+4y=2x^3	xy^{\prime\:}+4y=2x^{3}
tangent of y=sqrt(7x+2),(2,4)	tangent\:y=\sqrt{7x+2},(2,4)
integral of e^{-16x}	\int\:e^{-16x}dx
derivative of 1-e^{-x}sin(y)	\frac{d}{dx}(1-e^{-x}\sin(y))
derivative of sqrt(x/(x^2+5))	\frac{d}{dx}(\sqrt{\frac{x}{x^{2}+5}})
(\partial)/(\partial x)(1/(sqrt(x)))	\frac{\partial\:}{\partial\:x}(\frac{1}{\sqrt{x}})
integral of-e^{4x}+4x^5	\int\:-e^{4x}+4x^{5}dx
tangent of f(x)=sqrt(x),\at x=36	tangent\:f(x)=\sqrt{x},\at\:x=36
derivative of f(x)=4x^3+9	derivative\:f(x)=4x^{3}+9
(-x^{-2})^'	(-x^{-2})^{\prime\:}
(x^2+2x-1)y^'-(x+1)y=x-1	(x^{2}+2x-1)y^{\prime\:}-(x+1)y=x-1
integral of t^2(t^3-4)^2	\int\:t^{2}(t^{3}-4)^{2}dt
slope of (x-2)^4+e^{x-2}+(x-2*z)^2	slope\:(x-2)^{4}+e^{x-2}+(x-2\cdot\:z)^{2}
(dy)/(dx)=x+7y	\frac{dy}{dx}=x+7y
integral of 27x^{26}	\int\:27x^{26}dx
inverse oflaplace (-5s)/((s^2+1)^2)	inverselaplace\:\frac{-5s}{(s^{2}+1)^{2}}
limit as x approaches 1 of 3/(x-1)	\lim\:_{x\to\:1}(\frac{3}{x-1})
(\partial)/(\partial x)(sqrt(8-x^2))	\frac{\partial\:}{\partial\:x}(\sqrt{8-x^{2}})
integral from 1 to 100 of (21)/(x^3)	\int\:_{1}^{100}\frac{21}{x^{3}}dx
derivative of ln(x+sqrt(x^2-7))	derivative\:\ln(x+\sqrt{x^{2}-7})
2y^{''}-6y^'+5y=0	2y^{\prime\:\prime\:}-6y^{\prime\:}+5y=0
integral of cot(15x)	\int\:\cot(15x)dx
(\partial)/(\partial s)(sqrt(s^2+t^2))	\frac{\partial\:}{\partial\:s}(\sqrt{s^{2}+t^{2}})
sum from n=0 to infinity of nsin(n*pi)	\sum\:_{n=0}^{\infty\:}n\sin(n\cdot\:π)
inverse oflaplace (s+1)/((s(s^2+s+1)))	inverselaplace\:\frac{s+1}{(s(s^{2}+s+1))}
(\partial)/(\partial x)(e^{cos(x)})	\frac{\partial\:}{\partial\:x}(e^{\cos(x)})
derivative of (8x+9(9x-10))	\frac{d}{dx}((8x+9)(9x-10))
integral of x^2-4x+4	\int\:x^{2}-4x+4dx
(dy)/(dx)=(cos(12x))/(e^{12y)}	\frac{dy}{dx}=\frac{\cos(12x)}{e^{12y}}
integral from 1 to 2 of (15)/(x^3+5x)	\int\:_{1}^{2}\frac{15}{x^{3}+5x}dx
simplify xL(x)-x	simplify\:xL(x)-x
y^{''}-y^'-6y=0,y(0)=0,y^'(0)=4	y^{\prime\:\prime\:}-y^{\prime\:}-6y=0,y(0)=0,y^{\prime\:}(0)=4
limit as x approaches 2 of-6	\lim\:_{x\to\:2}(-6)
integral of 1/(9x^2-18x+72)	\int\:\frac{1}{9x^{2}-18x+72}dx
integral of-4ln(2x+1)	\int\:-4\ln(2x+1)dx
simplify (y^{-1}+y^{-2})(2y^{-3}-6y^{-4})	simplify\:(y^{-1}+y^{-2})(2y^{-3}-6y^{-4})
limit as x approaches infinity of 1/(x*log_{e)(x)}	\lim\:_{x\to\:\infty\:}(\frac{1}{x\cdot\:\log_{e}(x)})
limit as x approaches 2-of (x-2)/(x-2)	\lim\:_{x\to\:2-}(\frac{x-2}{x-2})
limit as x approaches infinity of 1+a/x	\lim\:_{x\to\:\infty\:}(1+\frac{a}{x})
integral of 3/((5v-1)^4)	\int\:\frac{3}{(5v-1)^{4}}dv
derivative of cos(x-x)	\frac{d}{dx}(\cos(x)-x)
tangent of (x-5)^2+(y-3)^2=18,(8,6)	tangent\:(x-5)^{2}+(y-3)^{2}=18,(8,6)
integral from 0 to 4 of pi(3x)^2	\int\:_{0}^{4}π(3x)^{2}dx
derivative of f(x)=cos(tan(x))	derivative\:f(x)=\cos(\tan(x))
y^{''}+ay^'+by=t+e^{3t}	y^{\prime\:\prime\:}+ay^{\prime\:}+by=t+e^{3t}
limit as x approaches-1 of ln(x+1)	\lim\:_{x\to\:-1}(\ln(x+1))
(\partial)/(\partial x)(1/2 (x^2+4y^2))	\frac{\partial\:}{\partial\:x}(\frac{1}{2}(x^{2}+4y^{2}))
(\partial)/(\partial x)(1/(sqrt(2x)))	\frac{\partial\:}{\partial\:x}(\frac{1}{\sqrt{2x}})
2xy(dy)/(dx)=y^2-x^2+1	2xy\frac{dy}{dx}=y^{2}-x^{2}+1
tangent of 100x^2+400x+5000,0.5	tangent\:100x^{2}+400x+5000,0.5
integral of e^{y(1-x)}	\int\:e^{y(1-x)}dx
derivative of y=7x^2cos(x)cot(x)	\frac{d}{dx}y=7x^{2}\cos(x)\cot(x)
(dy)/(dx)+e^xy=-9e^x	\frac{dy}{dx}+e^{x}y=-9e^{x}
integral of ((2x^3+3x))/(x^4+3x^2+7)	\int\:\frac{(2x^{3}+3x)}{x^{4}+3x^{2}+7}dx
(\partial)/(\partial x)(4xcos(4xy))	\frac{\partial\:}{\partial\:x}(4x\cos(4xy))
limit as x approaches 2+of-1/(x^2-4)	\lim\:_{x\to\:2+}(-\frac{1}{x^{2}-4})
integral of (tan(θ)sec(θ))	\int\:(\tan(θ)\sec(θ))dθ
integral of e^{2x-7}	\int\:e^{2x-7}dx
derivative of 4arcsin(x^3)	\frac{d}{dx}(4\arcsin(x^{3}))
derivative of 2/(\sqrt[3]{x^2)}	derivative\:\frac{2}{\sqrt[3]{x^{2}}}
derivative of (4csc(x)/(5^x))	\frac{d}{dx}(\frac{4\csc(x)}{5^{x}})
limit as x approaches infinity of n/(n!)	\lim\:_{x\to\:\infty\:}(\frac{n}{n!})
derivative of ln(49sin^2(x))	derivative\:\ln(49\sin^{2}(x))
(\partial)/(\partial v)(v^2)	\frac{\partial\:}{\partial\:v}(v^{2})
f(x)=(25)/x	f(x)=\frac{25}{x}
integral of 5sin(sqrt(x))	\int\:5\sin(\sqrt{x})dx
derivative of sqrt(x^2+y)	\frac{d}{dx}(\sqrt{x^{2}+y})
d/(dy)(t/(2y^4))	\frac{d}{dy}(\frac{t}{2y^{4}})
integral of 1/(sqrt(64x^2+1))	\int\:\frac{1}{\sqrt{64x^{2}+1}}dx
6x^2((dy)/(dx))=((dy)/(dx))+9xe^{-y}	6x^{2}(\frac{dy}{dx})=(\frac{dy}{dx})+9xe^{-y}
integral of 8x^{-3}	\int\:8x^{-3}dx
integral from 0 to 2 of e^{-x}	\int\:_{0}^{2}e^{-x}dx
integral of sqrt(3+x^2)	\int\:\sqrt{3+x^{2}}dx
integral of (3x^2-9x+2)	\int\:(3x^{2}-9x+2)dx
integral of sqrt((1+cos(x))/(1-cos(x)))	\int\:\sqrt{\frac{1+\cos(x)}{1-\cos(x)}}dx
derivative of arcsin(5x)	\frac{d}{dx}(\arcsin(5x))
derivative of 3/5 x^{5/3}-3/4 x^{1/3}+9	derivative\:\frac{3}{5}x^{\frac{5}{3}}-\frac{3}{4}x^{\frac{1}{3}}+9
limit as x approaches-2+of (1-x)/(x^3+8)	\lim\:_{x\to\:-2+}(\frac{1-x}{x^{3}+8})
limit as x approaches 1-of 2/(x-1)	\lim\:_{x\to\:1-}(\frac{2}{x-1})
(\partial)/(\partial x)((3x^2+y)e^{xy^2})	\frac{\partial\:}{\partial\:x}((3x^{2}+y)e^{xy^{2}})
laplacetransform (e^{2t}-e^t+t)^2	laplacetransform\:(e^{2t}-e^{t}+t)^{2}
derivative of 2x^2-7x-195	derivative\:2x^{2}-7x-195
integral of-cos((pit)/4)	\int\:-\cos(\frac{πt}{4})dt
limit as x approaches-2 of-x^2+6x-8	\lim\:_{x\to\:-2}(-x^{2}+6x-8)
integral of aarctan(bx)	\int\:a\arctan(bx)dx
limit as x approaches 1 of x^2+4	\lim\:_{x\to\:1}(x^{2}+4)
tangent of y=-0.02x^2-0.6x+90	tangent\:y=-0.02x^{2}-0.6x+90
derivative of 1/((x^2+1^3))	\frac{d}{dx}(\frac{1}{(x^{2}+1)^{3}})
integral of (e^{3x})/(e^{3x)+9}	\int\:\frac{e^{3x}}{e^{3x}+9}dx
integral from 0 to 1 of pi(6-3/2 x)^2	\int\:_{0}^{1}π(6-\frac{3}{2}x)^{2}dx
inverse oflaplace 2/(s^2+s)	inverselaplace\:\frac{2}{s^{2}+s}
y^{''}+9y=3cos(2x)+3	y^{\prime\:\prime\:}+9y=3\cos(2x)+3
integral of sqrt(9-x^2)(-2x)	\int\:\sqrt{9-x^{2}}(-2x)dx
derivative of (x-2^2(x+1))	\frac{d}{dx}((x-2)^{2}(x+1))
(\partial)/(\partial y)(x^2+y^2-9)	\frac{\partial\:}{\partial\:y}(x^{2}+y^{2}-9)
derivative of f(x)=6x^2+x-3	derivative\:f(x)=6x^{2}+x-3
laplacetransform t/2	laplacetransform\:\frac{t}{2}
area y=sqrt(x),x=9,y=0	area\:y=\sqrt{x},x=9,y=0
3y^{''}+5y^'+2y=0	3y^{\prime\:\prime\:}+5y^{\prime\:}+2y=0

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