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Popular Calculus Problems

(dy)/(dx)= x/y ,y(0)=-2	\frac{dy}{dx}=\frac{x}{y},y(0)=-2
inverse oflaplace 6/s+(24)/(s^2+16)	inverselaplace\:\frac{6}{s}+\frac{24}{s^{2}+16}
limit as x approaches 6 of 3/x	\lim\:_{x\to\:6}(\frac{3}{x})
derivative of (e^x/(e^x+2))	\frac{d}{dx}(\frac{e^{x}}{e^{x}+2})
integral of xsec^2(2x)	\int\:x\sec^{2}(2x)dx
maclaurin ln(1/(1-x))	maclaurin\:\ln(\frac{1}{1-x})
derivative of cos(10x-0.1sin(10x))	\frac{d}{dx}(\cos(10x)-0.1\sin(10x))
integral of 2/(x^2+3)	\int\:\frac{2}{x^{2}+3}dx
(x^2y^3-1/(1+9x^2))dx+(x^3y^2)dy=0	(x^{2}y^{3}-\frac{1}{1+9x^{2}})dx+(x^{3}y^{2})dy=0
derivative of sin^2(x-cos^2(x))	\frac{d}{dx}(\sin^{2}(x)-\cos^{2}(x))
derivative of ln(2x+1)	derivative\:\ln(2x+1)
limit as x approaches 5 of 3/(x-5)	\lim\:_{x\to\:5}(\frac{3}{x-5})
derivative of \|x\|^x	\frac{d}{dx}(\left\|x\right\|^{x})
integral of 1/(x-sqrt(x-2))	\int\:\frac{1}{x-\sqrt{x-2}}dx
(dy)/(dx)=((3x+2y))/(3x+2y+2)	\frac{dy}{dx}=\frac{(3x+2y)}{3x+2y+2}
(\partial)/(\partial x)(x^4+x*sin(y))	\frac{\partial\:}{\partial\:x}(x^{4}+x\cdot\:\sin(y))
integral of 1/(x(x-2))	\int\:\frac{1}{x(x-2)}dx
integral of (6400q)/(16q^2+3200)	\int\:\frac{6400q}{16q^{2}+3200}dq
derivative of (x^2(x^3-1)/(sqrt(x^2+1)))	\frac{d}{dx}(\frac{x^{2}(x^{3}-1)}{\sqrt{x^{2}+1}})
limit as x approaches 5 of 3x^2-4x-1	\lim\:_{x\to\:5}(3x^{2}-4x-1)
derivative of f(x)=8x+sqrt(x^2+7x+3)	derivative\:f(x)=8x+\sqrt{x^{2}+7x+3}
integral from 1 to 2 of y^3+1/(4y^3)	\int\:_{1}^{2}y^{3}+\frac{1}{4y^{3}}dy
maclaurin ln(1+4x^2+4x)	maclaurin\:\ln(1+4x^{2}+4x)
(\partial)/(\partial x)(e^{-x}sin(2y))	\frac{\partial\:}{\partial\:x}(e^{-x}\sin(2y))
(\partial)/(\partial y)(e^{xyz^5}yz^5)	\frac{\partial\:}{\partial\:y}(e^{xyz^{5}}yz^{5})
derivative of x+cos(x^2)	\frac{d}{dx}(x+\cos(x^{2}))
tangent of f(x)=x^2+x+9,\at x=2	tangent\:f(x)=x^{2}+x+9,\at\:x=2
integral of 5e^{3x}	\int\:5e^{3x}dx
extreme h(w)=((x+1)e^x)/(w-2)	extreme\:h(w)=\frac{(x+1)e^{x}}{w-2}
derivative of f(x)=5x^2-5x	derivative\:f(x)=5x^{2}-5x
integral of (2x)/(x-4)	\int\:\frac{2x}{x-4}dx
(x^2+5)dx+(y-3)(x-2)dy=0	(x^{2}+5)dx+(y-3)(x-2)dy=0
integral of 12tan^3(x)	\int\:12\tan^{3}(x)dx
integral from 0 to 1 of (42)/(4y-1)	\int\:_{0}^{1}\frac{42}{4y-1}dy
sum from n=2 to infinity of n*(3/4)^n	\sum\:_{n=2}^{\infty\:}n\cdot\:(\frac{3}{4})^{n}
y^{''}=6x+2,y(1)=-1,y^'(1)=7	y^{\prime\:\prime\:}=6x+2,y(1)=-1,y^{\prime\:}(1)=7
(\partial)/(\partial z)(arctan(x^2yz^2))	\frac{\partial\:}{\partial\:z}(\arctan(x^{2}yz^{2}))
(\partial)/(\partial z)(xarctan(yz))	\frac{\partial\:}{\partial\:z}(x\arctan(yz))
(\partial)/(\partial x)((2x+3y)^2)	\frac{\partial\:}{\partial\:x}((2x+3y)^{2})
limit as x approaches 0 of 1/(x-3)	\lim\:_{x\to\:0}(\frac{1}{x-3})
derivative of t/7	derivative\:\frac{t}{7}
derivative of 1/(sqrt(2x))	\frac{d}{dx}(\frac{1}{\sqrt{2x}})
inverse oflaplace 1/((s(s^2+6s-27)))	inverselaplace\:\frac{1}{(s(s^{2}+6s-27))}
(3v+v^2)/(v+1)=x(dv)/(dx)+v	\frac{3v+v^{2}}{v+1}=x\frac{dv}{dx}+v
(dy}{dx}=\frac{y+1)/x	\frac{dy}{dx}=\frac{y+1}{x}
derivative of 20+53e^{kt}	derivative\:20+53e^{kt}
derivative of (3x-1)/((x-1)^3)	derivative\:\frac{3x-1}{(x-1)^{3}}
integral of 6x+2	\int\:6x+2dx
derivative of (x+2)^3-e^{3x}	derivative\:(x+2)^{3}-e^{3x}
y^{''}+7y^'+10y=-20te^{4t}	y^{\prime\:\prime\:}+7y^{\prime\:}+10y=-20te^{4t}
f(x)= 1/(1+e^{-x)}	f(x)=\frac{1}{1+e^{-x}}
d/(dt)(1/2 {g}(t)t^2)	\frac{d}{dt}(\frac{1}{2}{g}(t)t^{2})
x^2(dy)/(dx)y^2=0	x^{2}\frac{dy}{dx}y^{2}=0
(\partial)/(\partial x)(Ae^{sqrt(-1)kx})	\frac{\partial\:}{\partial\:x}(Ae^{\sqrt{-1}kx})
integral of 2xln(3x)	\int\:2x\ln(3x)dx
sum from n=1 to infinity of 2pi^{-n}	\sum\:_{n=1}^{\infty\:}2π^{-n}
limit as x approaches infinity of (3^{3*x})/(3^x)	\lim\:_{x\to\:\infty\:}(\frac{3^{3\cdot\:x}}{3^{x}})
derivative of (x^5)/(5-x^4)	derivative\:\frac{x^{5}}{5-x^{4}}
(d^3)/(dx^3)(x^3)	\frac{d^{3}}{dx^{3}}(x^{3})
(\partial)/(\partial x)(x^{0.5}+y^{0.5})	\frac{\partial\:}{\partial\:x}(x^{0.5}+y^{0.5})
tangent of f(x)=(-8x)/(x^2+1),\at x=-1	tangent\:f(x)=\frac{-8x}{x^{2}+1},\at\:x=-1
derivative of x(2x-y^3)	\frac{d}{dx}(x(2x-y^{3}))
(d^2)/(dx^2)((x^2+10)^6)	\frac{d^{2}}{dx^{2}}((x^{2}+10)^{6})
sum from n=1 to infinity of 1/(3^n+1)	\sum\:_{n=1}^{\infty\:}\frac{1}{3^{n}+1}
derivative of 2x-3x^2	\frac{d}{dx}(2x-3x^{2})
(\partial)/(\partial y)(-2xy-y^4)	\frac{\partial\:}{\partial\:y}(-2xy-y^{4})
limit as x approaches 0 of (x-sin(x)}{e^x-1-x-\frac{x^2)/2}	\lim\:_{x\to\:0}(\frac{x-\sin(x)}{e^{x}-1-x-\frac{x^{2}}{2}})
derivative of y=e^{17x}	derivative\:y=e^{17x}
integral of (sqrt(y^2-100))/y	\int\:\frac{\sqrt{y^{2}-100}}{y}dy
integral of (24x^3-48x^2+5)/(x^2-2x)	\int\:\frac{24x^{3}-48x^{2}+5}{x^{2}-2x}dx
derivative of 1/(4x+3)	derivative\:\frac{1}{4x+3}
area x-x^2-x^2+6x,0,3.5	area\:x-x^{2}-x^{2}+6x,0,3.5
area y=x^2,y=0,x=1	area\:y=x^{2},y=0,x=1
integral of (sqrt(w^2-25))/(w^3)	\int\:\frac{\sqrt{w^{2}-25}}{w^{3}}dw
laplacetransform 0.03*(1-cos(2t))	laplacetransform\:0.03\cdot\:(1-\cos(2t))
limit as x approaches 0 of (2x^2)^{x^4}	\lim\:_{x\to\:0}((2x^{2})^{x^{4}})
d/(dn)((log_{10}(n))^3)	\frac{d}{dn}((\log_{10}(n))^{3})
integral of 1/(y(2-y))	\int\:\frac{1}{y(2-y)}dy
derivative of f(x)=ln((1-x)/(1+x))	derivative\:f(x)=\ln(\frac{1-x}{1+x})
(\partial)/(\partial x)((x+xy+y)^3)	\frac{\partial\:}{\partial\:x}((x+xy+y)^{3})
integral of x(3x^2-7)^{-2}	\int\:x(3x^{2}-7)^{-2}dx
derivative of 3/4 x^4-5x^2+4x+1	\frac{d}{dx}(\frac{3}{4}x^{4}-5x^{2}+4x+1)
derivative of cos^2(2-x^2)	\frac{d}{dx}(\cos^{2}(2-x^{2}))
t^2y^{''}-3ty^'+3y=0,y(1)=5,y^'(1)=3	t^{2}y^{\prime\:\prime\:}-3ty^{\prime\:}+3y=0,y(1)=5,y^{\prime\:}(1)=3
area 5cos(4x),5-5cos(4x),[0, pi/4 ]	area\:5\cos(4x),5-5\cos(4x),[0,\frac{π}{4}]
(\partial)/(\partial x)(2x-sqrt(4y^2+3z^2))	\frac{\partial\:}{\partial\:x}(2x-\sqrt{4y^{2}+3z^{2}})
limit as x approaches 0-of (-1/2)/(4x)	\lim\:_{x\to\:0-}(\frac{-\frac{1}{2}}{4x})
taylor e^{(-x^2)}	taylor\:e^{(-x^{2})}
integral of 5^{-sqrt(x-2)}	\int\:5^{-\sqrt{x-2}}dx
integral of 2xe^{-x^2}	\int\:2xe^{-x^{2}}dx
integral of 1/((x^2+4x+5)^2)	\int\:\frac{1}{(x^{2}+4x+5)^{2}}dx
integral of 1/((x+4)(x+8))	\int\:\frac{1}{(x+4)(x+8)}dx
slope ofintercept (3,-2),(7,0)	slopeintercept\:(3,-2),(7,0)
limit as x approaches 1 of (x-2)/(x^2-1)	\lim\:_{x\to\:1}(\frac{x-2}{x^{2}-1})
slope of (3.12)(5.6)	slope\:(3.12)(5.6)
y^{''}+y=7e^{-5x},y(0)=0,y^'(0)=0	y^{\prime\:\prime\:}+y=7e^{-5x},y(0)=0,y^{\prime\:}(0)=0
(\partial)/(\partial x)(4yx^3-15y^2x^4)	\frac{\partial\:}{\partial\:x}(4yx^{3}-15y^{2}x^{4})
d/(dt)(8sin(t))	\frac{d}{dt}(8\sin(t))
tangent of y=(-4x)/(x^2+1)	tangent\:y=\frac{-4x}{x^{2}+1}
taylor 5x^3-6x^2+12x-3,3	taylor\:5x^{3}-6x^{2}+12x-3,3

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