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Popular Calculus Problems
limit as x approaches 0+of 1+x^{(1/x)}
\lim\:_{x\to\:0+}(1+x^{(\frac{1}{x})})
integral from-2 to-1 of x-1/(x^2)
\int\:_{-2}^{-1}x-\frac{1}{x^{2}}dx
derivative of y=(9(1-sin(x)))/(2cos(x))
derivative\:y=\frac{9(1-\sin(x))}{2\cos(x)}
(\partial)/(\partial x)(ln(sqrt(xy)))
\frac{\partial\:}{\partial\:x}(\ln(\sqrt{xy}))
limit as x approaches 0 of e^{-1/(x^2)}
\lim\:_{x\to\:0}(e^{-\frac{1}{x^{2}}})
simplify 6/(2-4x)
simplify\:\frac{6}{2-4x}
derivative of xe^{x^2y}
\frac{d}{dx}(xe^{x^{2}y})
7x^2y^'=y^'+5xe^{-y}
7x^{2}y^{\prime\:}=y^{\prime\:}+5xe^{-y}
y^{''}-6y^'+9y=t^{-3}e^{3t}
y^{\prime\:\prime\:}-6y^{\prime\:}+9y=t^{-3}e^{3t}
((2xy+1))/y dx+((y-x))/(y^2)dy=0
\frac{(2xy+1)}{y}dx+\frac{(y-x)}{y^{2}}dy=0
tangent of sin(sin(x))
tangent\:\sin(\sin(x))
integral of (sin(x)cos^5(x))
\int\:(\sin(x)\cos^{5}(x))dx
(4cos(t))^'
(4\cos(t))^{\prime\:}
area y=4x^2,y=6x^2,y=6-5x
area\:y=4x^{2},y=6x^{2},y=6-5x
limit as x approaches 3 of 3x-6
\lim\:_{x\to\:3}(3x-6)
y=(x^x+1)^2
y=(x^{x}+1)^{2}
d/(dθ)(-n/2*ln(2pi)-n/2*ln(θ^2))
\frac{d}{dθ}(-\frac{n}{2}\cdot\:\ln(2π)-\frac{n}{2}\cdot\:\ln(θ^{2}))
limit as x approaches 0 of 7/(2x)
\lim\:_{x\to\:0}(\frac{7}{2x})
integral of 100-2x
\int\:100-2xdx
integral from 1 to 2 of (2x-5)^3
\int\:_{1}^{2}(2x-5)^{3}dx
derivative of ((x+2/(x-2))^2)
\frac{d}{dx}((\frac{x+2}{x-2})^{2})
integral of (x-sqrt(x)+1)(sqrt(x)+1)
\int\:(x-\sqrt{x}+1)(\sqrt{x}+1)dx
12x^3-3y^2sqrt(x^4+1)(dy)/(dx)=0
12x^{3}-3y^{2}\sqrt{x^{4}+1}\frac{dy}{dx}=0
(\partial)/(\partial x)(cos^5(x^3y^8))
\frac{\partial\:}{\partial\:x}(\cos^{5}(x^{3}y^{8}))
(d^2y)/(dx^2)=-y
\frac{d^{2}y}{dx^{2}}=-y
derivative of f(x)=x^2(3-x)^2
derivative\:f(x)=x^{2}(3-x)^{2}
limit as x approaches-1 of |x|-3
\lim\:_{x\to\:-1}(\left|x\right|-3)
integral of 8/(x(x+2)^3)
\int\:\frac{8}{x(x+2)^{3}}dx
derivative of sqrt(x)ln(2x)
\frac{d}{dx}(\sqrt{x}\ln(2x))
limit as x approaches 2+of x^2
\lim\:_{x\to\:2+}(x^{2})
derivative of b^x
derivative\:b^{x}
integral of (2x)/(sqrt(2x+1))
\int\:\frac{2x}{\sqrt{2x+1}}dx
xy^2+sqrt(1+x^2)(dy)/(dx)=0
xy^{2}+\sqrt{1+x^{2}}\frac{dy}{dx}=0
integral of x\sqrt[5]{64+x^2}
\int\:x\sqrt[5]{64+x^{2}}dx
f(x)= 6/x
f(x)=\frac{6}{x}
slope of (10,x),(8,10)
slope\:(10,x),(8,10)
derivative of y=(6x^2+8x+6)/(sqrt(x))
derivative\:y=\frac{6x^{2}+8x+6}{\sqrt{x}}
area x+2,-1,2,5
area\:x+2,-1,2,5
(d^6)/(dx^6)(x^{-3})
\frac{d^{6}}{dx^{6}}(x^{-3})
derivative of 4sqrt(x)-6/(\sqrt[3]{x^2})
\frac{d}{dx}(4\sqrt{x}-\frac{6}{\sqrt[3]{x^{2}}})
derivative of (e^{-x}-e^3(e^x+e^{-5}))
\frac{d}{dx}((e^{-x}-e^{3})(e^{x}+e^{-5}))
(d^4)/(dx^4)(e^{1/x})
\frac{d^{4}}{dx^{4}}(e^{\frac{1}{x}})
derivative of y=ln(sin(x))
derivative\:y=\ln(\sin(x))
derivative of x^2sqrt(7x-5)
\frac{d}{dx}(x^{2}\sqrt{7x-5})
derivative of |x-9|
\frac{d}{dx}(\left|x-9\right|)
y^{''}-2y^'+37y=0
y^{\prime\:\prime\:}-2y^{\prime\:}+37y=0
limit as x approaches 0+of (x^x-1)/x
\lim\:_{x\to\:0+}(\frac{x^{x}-1}{x})
(dy)/(dx)=sec(x)+ytan(x)
\frac{dy}{dx}=\sec(x)+y\tan(x)
integral of 2/9 x^{-1/9}
\int\:\frac{2}{9}x^{-\frac{1}{9}}dx
slope of f(x)=x^4-20x^2+64
slope\:f(x)=x^{4}-20x^{2}+64
integral of (sin^4(3x)cos^3(3x))
\int\:(\sin^{4}(3x)\cos^{3}(3x))dx
limit as x approaches-infinity of 6-2^x
\lim\:_{x\to\:-\infty\:}(6-2^{x})
integral from-1 to 2 of (2+x-x^2)^2
\int\:_{-1}^{2}(2+x-x^{2})^{2}dx
(\partial)/(\partial y)(x^2-2xy)
\frac{\partial\:}{\partial\:y}(x^{2}-2xy)
limit as x approaches-3 of (x-7)/(x+3)
\lim\:_{x\to\:-3}(\frac{x-7}{x+3})
tangent of 1+sqrt((x\at (4.3)))
tangent\:1+\sqrt{(x\at\:(4.3))}
(\partial)/(\partial z)(4xz)
\frac{\partial\:}{\partial\:z}(4xz)
derivative of (x^2+2/(x^2-3))
\frac{d}{dx}(\frac{x^{2}+2}{x^{2}-3})
y^'-y=e^x
y^{\prime\:}-y=e^{x}
derivative of y=ln^3(sqrt(a^2+1))
derivative\:y=\ln^{3}(\sqrt{a^{2}+1})
area 2x^2+2,(1,3)
area\:2x^{2}+2,(1,3)
derivative of 1/(cos(2x))
\frac{d}{dx}(\frac{1}{\cos(2x)})
integral of x^2sqrt(4-x)
\int\:x^{2}\sqrt{4-x}dx
derivative of (9x^3-4ln(x)(7e^x+8x))
\frac{d}{dx}((9x^{3}-4\ln(x))(7e^{x}+8x))
(\partial)/(\partial y)(ln(x/t))
\frac{\partial\:}{\partial\:y}(\ln(\frac{x}{t}))
integral of xe^{-yx}
\int\:xe^{-yx}dx
derivative of sin^2(x^2+1)
\frac{d}{dx}(\sin^{2}(x^{2}+1))
integral from 1 to 4 of-5sqrt(t)ln(t)
\int\:_{1}^{4}-5\sqrt{t}\ln(t)dt
(\partial)/(\partial x)(x^2cos(xy^2))
\frac{\partial\:}{\partial\:x}(x^{2}\cos(xy^{2}))
limit as t approaches+0 of (e^t-1)/(t^9)
\lim\:_{t\to\:+0}(\frac{e^{t}-1}{t^{9}})
tangent of f(x)= 3/x ,(6, 1/2)
tangent\:f(x)=\frac{3}{x},(6,\frac{1}{2})
integral of 32sin^4(2x)
\int\:32\sin^{4}(2x)dx
d/(dy)((x^2+y^2)arctan(y/x))
\frac{d}{dy}((x^{2}+y^{2})\arctan(\frac{y}{x}))
taylor e^x,x=2
taylor\:e^{x},x=2
integral of x/7
\int\:\frac{x}{7}dx
y^'-5y=10x
y^{\prime\:}-5y=10x
inverse oflaplace 1/((s-4)^2)
inverselaplace\:\frac{1}{(s-4)^{2}}
integral of 4/(25-x)
\int\:\frac{4}{25-x}dx
derivative of f(x)=294x^5-120x^4+420x^2
derivative\:f(x)=294x^{5}-120x^{4}+420x^{2}
tangent of f(x)=3x^2+4x,\at x=-3
tangent\:f(x)=3x^{2}+4x,\at\:x=-3
integral of 7/(2y^4)
\int\:\frac{7}{2y^{4}}dy
y^'=(x^4y^4+4x^4)/(y^3)
y^{\prime\:}=\frac{x^{4}y^{4}+4x^{4}}{y^{3}}
tangent of x^3+2x^2+4
tangent\:x^{3}+2x^{2}+4
integral of (4^{sqrt(x)})/(sqrt(x))
\int\:\frac{4^{\sqrt{x}}}{\sqrt{x}}dx
y^{''}+9y=4sin(x)
y^{\prime\:\prime\:}+9y=4\sin(x)
derivative of 1+sqrt(5x)
\frac{d}{dx}(1+\sqrt{5x})
(\partial)/(\partial x)(3e^{-y}(x^2+y^2)+4)
\frac{\partial\:}{\partial\:x}(3e^{-y}(x^{2}+y^{2})+4)
integral of 1/(x(x^2-16)^{3/2)}
\int\:\frac{1}{x(x^{2}-16)^{\frac{3}{2}}}dx
derivative of f(x)=(cos(x))/(1+asin(x))
derivative\:f(x)=\frac{\cos(x)}{1+a\sin(x)}
derivative of y=sin(ln(x))
derivative\:y=\sin(\ln(x))
integral from 0 to 1 of x^2
\int\:_{0}^{1}x^{2}dx
(\partial)/(\partial x)(xe^{xy}cos(2x)-3)
\frac{\partial\:}{\partial\:x}(xe^{xy}\cos(2x)-3)
(dx)/(dt)=cot(x)cos(t)
\frac{dx}{dt}=\cot(x)\cos(t)
derivative of (x+1)e^x
derivative\:(x+1)e^{x}
f(x)= 5/(x^2)
f(x)=\frac{5}{x^{2}}
derivative of sqrt(x)(3x^2+4x-9)
\frac{d}{dx}(\sqrt{x}(3x^{2}+4x-9))
y^{''}+9y=5t^4,y(0)=0,y^'(0)=0
y^{\prime\:\prime\:}+9y=5t^{4},y(0)=0,y^{\prime\:}(0)=0
derivative of sqrt(arcsech(x))
\frac{d}{dx}(\sqrt{\arcsech(x)})
(\partial)/(\partial x)(6x^{1/2}+2y)
\frac{\partial\:}{\partial\:x}(6x^{\frac{1}{2}}+2y)
limit as x approaches 0 of sin(x)ln(4x)
\lim\:_{x\to\:0}(\sin(x)\ln(4x))
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