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Popular Calculus Problems

integral of (x^4+3x^2+5)/(x^4)	\int\:\frac{x^{4}+3x^{2}+5}{x^{4}}dx
(dx)/(dt)=8+4sin(t/4)-x/(100),x(0)=70	\frac{dx}{dt}=8+4\sin(\frac{t}{4})-\frac{x}{100},x(0)=70
tangent of f(x)=(sqrt(x))/(2x-8),\at x=3	tangent\:f(x)=\frac{\sqrt{x}}{2x-8},\at\:x=3
limit as x approaches infinity of 5/x-4	\lim\:_{x\to\:\infty\:}(\frac{5}{x}-4)
derivative of y=(ln(x))/(x^9)	derivative\:y=\frac{\ln(x)}{x^{9}}
integral of 1/2 ln(x)	\int\:\frac{1}{2}\ln(x)dx
derivative of-8e^{-x}	\frac{d}{dx}(-8e^{-x})
4x^{''}+2x^'+4x=100,x(0)=5,x^'(0)=0	4x^{\prime\:\prime\:}+2x^{\prime\:}+4x=100,x(0)=5,x^{\prime\:}(0)=0
limit as x approaches 3 of sqrt(5x^2+2x)	\lim\:_{x\to\:3}(\sqrt{5x^{2}+2x})
x*(dy)/(dx)+y=e^{-x}	x\cdot\:\frac{dy}{dx}+y=e^{-x}
derivative of f(x)=(-8x)/(x^2+1)	derivative\:f(x)=\frac{-8x}{x^{2}+1}
derivative of (4+3x/(x^2-2x))	\frac{d}{dx}(\frac{4+3x}{x^{2}-2x})
(x+xy^2)dx+e^{x^2}ydy=0	(x+xy^{2})dx+e^{x^{2}}ydy=0
integral from-2 to x^2-3x of e^{t^2}	\int\:_{-2}^{x^{2}-3x}e^{t^{2}}dt
derivative of y=x^{4/5}(x-3)	derivative\:y=x^{\frac{4}{5}}(x-3)
derivative of (-2x^2+25/(sqrt(25-x^2)))	\frac{d}{dx}(\frac{-2x^{2}+25}{\sqrt{25-x^{2}}})
d/(dθ)(cos^2(θ)-sin^2(θ))	\frac{d}{dθ}(\cos^{2}(θ)-\sin^{2}(θ))
d/(dt)(8te^{-t})	\frac{d}{dt}(8te^{-t})
integral of cos(y/x)	\int\:\cos(\frac{y}{x})dx
sum from n=0 to infinity of (-1/3)^n	\sum\:_{n=0}^{\infty\:}(-\frac{1}{3})^{n}
(xy^'-1)ln(x)=2y	(xy^{\prime\:}-1)\ln(x)=2y
sum from n=0 to infinity of 1/((2n+3)^3)	\sum\:_{n=0}^{\infty\:}\frac{1}{(2n+3)^{3}}
derivative of f(x)= 3/(sqrt(11-x))	derivative\:f(x)=\frac{3}{\sqrt{11-x}}
(\partial)/(\partial y)(e^{4y-x^2-y^2})	\frac{\partial\:}{\partial\:y}(e^{4y-x^{2}-y^{2}})
derivative of 5/(x^4)+\sqrt[3]{x^2}	derivative\:\frac{5}{x^{4}}+\sqrt[3]{x^{2}}
derivative of (2xy/(x+y))	\frac{d}{dx}(\frac{2xy}{x+y})
derivative of sqrt(154)	\frac{d}{dx}(\sqrt{154})
derivative of ((4x^2)/(4-x))^3	derivative\:(\frac{4x^{2}}{4-x})^{3}
(dy)/(dx)=(x-y)/(x+y)	\frac{dy}{dx}=\frac{x-y}{x+y}
derivative of (1/(y^2)-3/(y^4))(y+5y^3)	derivative\:(\frac{1}{y^{2}}-\frac{3}{y^{4}})(y+5y^{3})
limit as x approaches infinity of y	\lim\:_{x\to\:\infty\:}(y)
(\partial)/(\partial x)(x*e^{y/x})	\frac{\partial\:}{\partial\:x}(x\cdot\:e^{\frac{y}{x}})
integral of (y^2)/x	\int\:\frac{y^{2}}{x}dx
tangent of f(x)=x^4-13^2+36,\at x=3	tangent\:f(x)=x^{4}-13^{2}+36,\at\:x=3
limit as x approaches 1 of (3x-2)/(x+2)	\lim\:_{x\to\:1}(\frac{3x-2}{x+2})
limit as x approaches 4-of x^2+1	\lim\:_{x\to\:4-}(x^{2}+1)
y^'=(xy^3)/(sqrt(1+x^2))	y^{\prime\:}=\frac{xy^{3}}{\sqrt{1+x^{2}}}
integral of (e^{4x})/(e^{4x)+6}	\int\:\frac{e^{4x}}{e^{4x}+6}dx
sum from n=1 to infinity of 5/(2^n)	\sum\:_{n=1}^{\infty\:}\frac{5}{2^{n}}
tangent of y=(2x)/(x+1),\at x=1	tangent\:y=\frac{2x}{x+1},\at\:x=1
2(dy)/(dx)+4y=1	2\frac{dy}{dx}+4y=1
taylor f(x)=cos(x^4)	taylor\:f(x)=\cos(x^{4})
derivative of y=t	derivative\:y=t
limit as x approaches 0 of sin^5(2x^2)	\lim\:_{x\to\:0}(\sin^{5}(2x^{2}))
derivative of x^3-3x+6	\frac{d}{dx}(x^{3}-3x+6)
derivative of e^{-2x+1}	\frac{d}{dx}(e^{-2x+1})
derivative of g(t)= 3/(sqrt(t))	derivative\:g(t)=\frac{3}{\sqrt{t}}
slope of f(x)= 3/(x-1)	slope\:f(x)=\frac{3}{x-1}
y^{''}+(2/x)y^'=2x+4	y^{\prime\:\prime\:}+(\frac{2}{x})y^{\prime\:}=2x+4
(x+ye^{y/x})dx-xe^{y/x}dy=0,y(1)=0	(x+ye^{\frac{y}{x}})dx-xe^{\frac{y}{x}}dy=0,y(1)=0
derivative of arccsc(sqrt(x))	\frac{d}{dx}(\arccsc(\sqrt{x}))
inverse oflaplace (2s+1)/(s^2+2s+1)	inverselaplace\:\frac{2s+1}{s^{2}+2s+1}
derivative of me^{mx}	\frac{d}{dx}(me^{mx})
limit as x approaches 0 of xsqrt(1+1/2)	\lim\:_{x\to\:0}(x\sqrt{1+\frac{1}{2}})
(\partial}{\partial v}(\frac{u-v)/2)	\frac{\partial\:}{\partial\:v}(\frac{u-v}{2})
sum from n=0 to infinity of (n+5)/(5^n)	\sum\:_{n=0}^{\infty\:}\frac{n+5}{5^{n}}
y'=0.1(5-y)y	y\prime\:=0.1(5-y)y
integral of (3ln(x))/x	\int\:\frac{3\ln(x)}{x}dx
(\partial)/(\partial x)(-2y(-2x-y+6))	\frac{\partial\:}{\partial\:x}(-2y(-2x-y+6))
integral from-8 to 0 of 1/(sqrt(1-x))	\int\:_{-8}^{0}\frac{1}{\sqrt{1-x}}dx
d/(d{z)}(({y})/(sqrt({x)^2+{y)^2+{z}^2}})	\frac{d}{d{z}}(\frac{{y}}{\sqrt{{x}^{2}+{y}^{2}+{z}^{2}}})
integral of 9arctan(sqrt(x))	\int\:9\arctan(\sqrt{x})dx
derivative of 8718e(587x)	\frac{d}{dx}(8718e(587x))
slope of (x^2)/(x+8)	slope\:\frac{x^{2}}{x+8}
derivative of 1/(5-x)	derivative\:\frac{1}{5-x}
inverse oflaplace (1/(2^{1-s)})*e^{-as}	inverselaplace\:(\frac{1}{2^{1-s}})\cdot\:e^{-as}
integral of (x^2+3)/x	\int\:\frac{x^{2}+3}{x}dx
limit as x approaches-2+of (5x)/(2+x)	\lim\:_{x\to\:-2+}(\frac{5x}{2+x})
f(x)= 1/20 sin(5x^2)-1/4 sin(x^2)	f(x)=\frac{1}{20}\sin(5x^{2})-\frac{1}{4}\sin(x^{2})
slope of y=4x-3x^2	slope\:y=4x-3x^{2}
tangent of f(x)=3x^2+2x-5,(2,7)	tangent\:f(x)=3x^{2}+2x-5,(2,7)
integral of 15e^{-31t}t	\int\:15e^{-31t}tdt
d/(dt)(20(1-e^{-t/2}))	\frac{d}{dt}(20(1-e^{-\frac{t}{2}}))
derivative of \sqrt[3]{y}*\sqrt[4]{x^3}	\frac{d}{dx}(\sqrt[3]{y}\cdot\:\sqrt[4]{x^{3}})
derivative of (e^x-4)/(ln\|x\|)	derivative\:\frac{e^{x}-4}{\ln\left\|x\right\|}
integral of 4/(tsqrt(t^2+36))	\int\:\frac{4}{t\sqrt{t^{2}+36}}dt
integral of sqrt(x^2+2x^4)	\int\:\sqrt{x^{2}+2x^{4}}dx
derivative of (sin^5(x)/5-(sin^7(x))/7)	\frac{d}{dx}(\frac{\sin^{5}(x)}{5}-\frac{\sin^{7}(x)}{7})
derivative of e^x-cos(x)	\frac{d}{dx}(e^{x}-\cos(x))
derivative of y=(2x+1)(x+5)^3	derivative\:y=(2x+1)(x+5)^{3}
sum from n=0 to infinity of (-1)^n(2^n)	\sum\:_{n=0}^{\infty\:}(-1)^{n}(2^{n})
derivative of-1/(3x^3)	\frac{d}{dx}(-\frac{1}{3x^{3}})
derivative of y=30e^{-0.0000323(1600)}	derivative\:y=30e^{-0.0000323(1600)}
(\partial)/(\partial x)(tan(y/x))	\frac{\partial\:}{\partial\:x}(\tan(\frac{y}{x}))
area \|x\|,x^2	area\:\left\|x\right\|,x^{2}
integral of (sqrt(x^{11)})	\int\:(\sqrt{x^{11}})dx
derivative of x/((x-4^2))	\frac{d}{dx}(\frac{x}{(x-4)^{2}})
area 3x, 1/3 x,0,4	area\:3x,\frac{1}{3}x,0,4
derivative of x^3ln(1+x)	\frac{d}{dx}(x^{3}\ln(1+x))
integral from 1 to 3 of 11r^3ln(r)	\int\:_{1}^{3}11r^{3}\ln(r)dr
y^{''}+25y=40sin(5t)	y^{\prime\:\prime\:}+25y=40\sin(5t)
(\partial)/(\partial y)(xy+y)	\frac{\partial\:}{\partial\:y}(xy+y)
laplacetransform 10e^{(-10t)}	laplacetransform\:10e^{(-10t)}
integral of e^{4x}x	\int\:e^{4x}xdx
derivative of f(x)=4sqrt(6x^2+7)	derivative\:f(x)=4\sqrt{6x^{2}+7}
(\partial)/(\partial x)(sin(x)+sin(y))	\frac{\partial\:}{\partial\:x}(\sin(x)+\sin(y))
integral of 4x+sqrt(x)	\int\:4x+\sqrt{x}dx
slope of 5x^3+10x^2-2x+1	slope\:5x^{3}+10x^{2}-2x+1
derivative of x^2-2x+1	derivative\:x^{2}-2x+1
2xy+6x+(x^2-4)y^'=0	2xy+6x+(x^{2}-4)y^{\prime\:}=0

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