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Popular Calculus Problems
(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}})
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 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}))
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
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 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))}
(dy}{dx}=\frac{y+1)/x
\frac{dy}{dx}=\frac{y+1}{x}
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}
(\partial)/(\partial x)(Ae^{sqrt(-1)kx})
\frac{\partial\:}{\partial\:x}(Ae^{\sqrt{-1}kx})
integral of 2xln(3x)
\int\:2x\ln(3x)dx
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})
derivative of x(2x-y^3)
\frac{d}{dx}(x(2x-y^{3}))
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}})
integral of (sqrt(y^2-100))/y
\int\:\frac{\sqrt{y^{2}-100}}{y}dy
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 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 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
derivative of 4x^3+3x^2-6x+1
\frac{d}{dx}(4x^{3}+3x^{2}-6x+1)
limit as x approaches 0+of 4/(x^2-x)
\lim\:_{x\to\:0+}(\frac{4}{x^{2}-x})
(\partial)/(\partial y)(ye^{xy}+y)
\frac{\partial\:}{\partial\:y}(ye^{xy}+y)
derivative of x^3-5x^2+13
derivative\:x^{3}-5x^{2}+13
derivative of e^{sin(sqrt(x)})
\frac{d}{dx}(e^{\sin(\sqrt{x})})
integral of e^{2x}+x^3
\int\:e^{2x}+x^{3}dx
limit as x approaches 1 of 10x
\lim\:_{x\to\:1}(10x)
sum from n=0 to infinity of 7x^{3n}
\sum\:_{n=0}^{\infty\:}7x^{3n}
(dy)/(dx)=((y^2+1))/(x^2+1)
\frac{dy}{dx}=\frac{(y^{2}+1)}{x^{2}+1}
integral of x^3sqrt(x^2+22)
\int\:x^{3}\sqrt{x^{2}+22}dx
y^{''}+4pi^2y=cos^3(2pix),y(10)=2
y^{\prime\:\prime\:}+4π^{2}y=\cos^{3}(2πx),y(10)=2
area y^2=x+1,x=3
area\:y^{2}=x+1,x=3
limit as x approaches 2-of (x-3)/(x+2)
\lim\:_{x\to\:2-}(\frac{x-3}{x+2})
derivative of f(x)= 1/x+1/(1-x)
derivative\:f(x)=\frac{1}{x}+\frac{1}{1-x}
integral of (x^3)/((5x+2)^3)
\int\:\frac{x^{3}}{(5x+2)^{3}}dx
integral of (e^x)/(e^x+3)
\int\:\frac{e^{x}}{e^{x}+3}dx
integral of sin(3x)sin(4x)
\int\:\sin(3x)\sin(4x)dx
derivative of (sqrt(x^2+1)/(\sqrt[3]{x^2+1)})
\frac{d}{dx}(\frac{\sqrt{x^{2}+1}}{\sqrt[3]{x^{2}+1}})
integral of (x^3+3)^{1/4}x^5
\int\:(x^{3}+3)^{\frac{1}{4}}x^{5}dx
integral of 3(x+5)e^{4x}
\int\:3(x+5)e^{4x}dx
f(x)=x^2-2x-2sin(x-2)
f(x)=x^{2}-2x-2\sin(x-2)
limit as x approaches 1-of (2x+1)/(x-1)
\lim\:_{x\to\:1-}(\frac{2x+1}{x-1})
integral of (4e^x+12x^3+4x)
\int\:(4e^{x}+12x^{3}+4x)dx
(d^2)/(dx^2)(3ln(sec(x)+tan(x)))
\frac{d^{2}}{dx^{2}}(3\ln(\sec(x)+\tan(x)))
integral from-1 to 1 of cos(x)
\int\:_{-1}^{1}\cos(x)dx
y^{''}+2y=e^x+x^3
y^{\prime\:\prime\:}+2y=e^{x}+x^{3}
integral of (e^x)/(sqrt(1-4e^{2x))}
\int\:\frac{e^{x}}{\sqrt{1-4e^{2x}}}dx
inverse oflaplace (1.5)/(((s+1)))
inverselaplace\:\frac{1.5}{((s+1))}
y^'=e^{4y}sin(5x)
y^{\prime\:}=e^{4y}\sin(5x)
d/(dθ)(sin(3θ))
\frac{d}{dθ}(\sin(3θ))
integral of x^2a^{2x}
\int\:x^{2}a^{2x}dx
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