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Popular Calculus Problems
derivative of f(x)=4x^6-5x^{-5}+3sqrt(x)-6/(x^4)-5e^x
derivative\:f(x)=4x^{6}-5x^{-5}+3\sqrt{x}-\frac{6}{x^{4}}-5e^{x}
derivative of cos(3x+2-(2x+1)^{-3})
\frac{d}{dx}(\cos(3x+2)-(2x+1)^{-3})
integral of (sin(y))/x
\int\:\frac{\sin(y)}{x}dx
integral from 0 to 1 of \sqrt[3]{1+7x}
\int\:_{0}^{1}\sqrt[3]{1+7x}dx
derivative of f(x)= r/(sqrt(r^2+5))
derivative\:f(x)=\frac{r}{\sqrt{r^{2}+5}}
derivative of {g}(x(x^3))
\frac{d}{dx}({g}(x)(x^{3}))
(\partial)/(\partial x)(yx^2+6x^3+xy)
\frac{\partial\:}{\partial\:x}(yx^{2}+6x^{3}+xy)
(\partial)/(\partial x)(x^2+y^2+x^2y+4)
\frac{\partial\:}{\partial\:x}(x^{2}+y^{2}+x^{2}y+4)
derivative of sqrt(3x^2+5x+8)
\frac{d}{dx}(\sqrt{3x^{2}+5x+8})
integral of cos(6t)
\int\:\cos(6t)dt
area 4sqrt(2x),2x^2,-4x+6
area\:4\sqrt{2x},2x^{2},-4x+6
(t+2)y'+y= 1/(t-1)
(t+2)y\prime\:+y=\frac{1}{t-1}
(\partial)/(\partial l)(2pisqrt(l/({g))})
\frac{\partial\:}{\partial\:l}(2π\sqrt{\frac{l}{{g}}})
16y^{''}-pi^2y=0
16y^{\prime\:\prime\:}-π^{2}y=0
integral of x^2sqrt(x^3+15)
\int\:x^{2}\sqrt{x^{3}+15}dx
sum from n=1 to infinity of e^{(-n^2)}
\sum\:_{n=1}^{\infty\:}e^{(-n^{2})}
limit as x approaches-5 of-9/(x+5)
\lim\:_{x\to\:-5}(-\frac{9}{x+5})
derivative of ln(sqrt((x^2-1/(x^2+1))))
\frac{d}{dx}(\ln(\sqrt{\frac{x^{2}-1}{x^{2}+1}}))
integral of (5+x)
\int\:(5+x)dx
(dy)/(dx)=((2xy+2x))/(x^2+1)
\frac{dy}{dx}=\frac{(2xy+2x)}{x^{2}+1}
limit as x approaches 3 of 4x-a+b
\lim\:_{x\to\:3}(4x-a+b)
integral from 0 to 1 of 7e^x-7xe^{x^2}
\int\:_{0}^{1}7e^{x}-7xe^{x^{2}}dx
derivative of sin(pi/2 x)
\frac{d}{dx}(\sin(\frac{π}{2}x))
integral from 0 to 6 of (7t)/((t-7)^2)
\int\:_{0}^{6}\frac{7t}{(t-7)^{2}}dt
inverse oflaplace (e^{-4s})/(s^2)
inverselaplace\:\frac{e^{-4s}}{s^{2}}
tangent of 98.284e^{-0.28x}
tangent\:98.284e^{-0.28x}
integral from 0 to 1 of 10^x
\int\:_{0}^{1}10^{x}dx
limit as x approaches 2 of 4tan(3x-3)
\lim\:_{x\to\:2}(4\tan(3x-3))
implicit (dy)/(dx),xcos(5y)+y^5e^{6x}=e^{2x}
implicit\:\frac{dy}{dx},x\cos(5y)+y^{5}e^{6x}=e^{2x}
sum from n=2 to infinity of 1
\sum\:_{n=2}^{\infty\:}1
integral of (sin(x))/((1-cos(x))^3)
\int\:\frac{\sin(x)}{(1-\cos(x))^{3}}dx
(\partial)/(\partial x)(3x^2y-x+2y^3)
\frac{\partial\:}{\partial\:x}(3x^{2}y-x+2y^{3})
tangent of 2x^3-4x^2
tangent\:2x^{3}-4x^{2}
integral of cos(4x)cos(8x)
\int\:\cos(4x)\cos(8x)dx
derivative of 6/(3x^5+2/(5x^2)-7/(9x))
\frac{d}{dx}(\frac{6}{3x^{5}}+\frac{2}{5x^{2}}-\frac{7}{9x})
(y^2-x^2)dx+(-2xy)dy=0
(y^{2}-x^{2})dx+(-2xy)dy=0
y^{''}-4y^'-12y=8e^{-2x}
y^{\prime\:\prime\:}-4y^{\prime\:}-12y=8e^{-2x}
derivative of xe^xcos(x)
\frac{d}{dx}(xe^{x}\cos(x))
integral of (5x^2+2x^3)
\int\:(5x^{2}+2x^{3})dx
x((dy)/(dx))=xtan(y/x)+y
x(\frac{dy}{dx})=x\tan(\frac{y}{x})+y
integral of (3x+5)^6
\int\:(3x+5)^{6}dx
(\partial)/(\partial x)(5cos(5x))
\frac{\partial\:}{\partial\:x}(5\cos(5x))
limit as x approaches 0+of x/(|x|)
\lim\:_{x\to\:0+}(\frac{x}{\left|x\right|})
integral from 0 to 1 of 2pi(x+10)(x^2)
\int\:_{0}^{1}2π(x+10)(x^{2})dx
(\partial)/(\partial x)(xye^{xyz})
\frac{\partial\:}{\partial\:x}(xye^{xyz})
integral of t+1
\int\:t+1dt
limit as x approaches 0-of 1+x^2
\lim\:_{x\to\:0-}(1+x^{2})
derivative of f(x)=\sqrt[7]{x^6}-x^pi
derivative\:f(x)=\sqrt[7]{x^{6}}-x^{π}
implicit (dy)/(dx),x^{(2/3)}+y^{(2/3)}=10
implicit\:\frac{dy}{dx},x^{(\frac{2}{3})}+y^{(\frac{2}{3})}=10
f(t)=8cos(t)
f(t)=8\cos(t)
(\partial)/(\partial x)((2x)/(x+1))
\frac{\partial\:}{\partial\:x}(\frac{2x}{x+1})
derivative of Y(θ)=cot^2(cos(θ))
derivative\:Y(θ)=\cot^{2}(\cos(θ))
derivative of f(t)=6t-5t^2
derivative\:f(t)=6t-5t^{2}
(\partial)/(\partial x)(e^{-4x-x^2+2y-y^2})
\frac{\partial\:}{\partial\:x}(e^{-4x-x^{2}+2y-y^{2}})
taylor 1/(x+2)
taylor\:\frac{1}{x+2}
limit as x approaches+0+of (x^2)/6-5/x
\lim\:_{x\to\:+0+}(\frac{x^{2}}{6}-\frac{5}{x})
derivative of (x^3+6e^x)
\frac{d}{dx}((x^{3}+6)e^{x})
derivative of sinh(0)
\frac{d}{dx}(\sinh(0))
tangent of f(x)=x^2,\at x=3,x=7
tangent\:f(x)=x^{2},\at\:x=3,x=7
integral from 1 to 5 of 4/(x^2+4x+4)
\int\:_{1}^{5}\frac{4}{x^{2}+4x+4}dx
(dv)/(dt)= 1/(t^2)
\frac{dv}{dt}=\frac{1}{t^{2}}
limit as x approaches 8-of (x^8)/(x-8)
\lim\:_{x\to\:8-}(\frac{x^{8}}{x-8})
derivative of 30e^{-(x^2/3})
\frac{d}{dx}(30e^{-\frac{x^{2}}{3}})
(\partial)/(\partial y)(e^y(y^2-x^2))
\frac{\partial\:}{\partial\:y}(e^{y}(y^{2}-x^{2}))
integral of 5/((3x-4)^2)
\int\:\frac{5}{(3x-4)^{2}}dx
tangent of 3-2cos(x),\at x= pi/2
tangent\:3-2\cos(x),\at\:x=\frac{π}{2}
integral of 1/12 ln^2(3x+1)
\int\:\frac{1}{12}\ln^{2}(3x+1)dx
integral of 1/(2+2x^2)
\int\:\frac{1}{2+2x^{2}}dx
derivative of 1-1/t
derivative\:1-\frac{1}{t}
derivative of x^2+5x+\sqrt[3]{x^2-4}
\frac{d}{dx}(x^{2}+5x+\sqrt[3]{x^{2}-4})
integral of 8/(8+e^x)
\int\:\frac{8}{8+e^{x}}dx
slope of y^2=9x,\at x=16
slope\:y^{2}=9x,\at\:x=16
integral of 2/(2+2x)
\int\:\frac{2}{2+2x}dx
tangent of f(x)=-5x^2+6,\at x=5
tangent\:f(x)=-5x^{2}+6,\at\:x=5
limit as x approaches-3 of sqrt(4x+28-4)
\lim\:_{x\to\:-3}(\sqrt{4x+28-4})
derivative of (7sqrt(x)/(2x^3))
\frac{d}{dx}(\frac{7\sqrt{x}}{2x^{3}})
derivative of (x^3+2^2(x^5+4)^4)
\frac{d}{dx}((x^{3}+2)^{2}(x^{5}+4)^{4})
f(x)=1-\sqrt[3]{x^2}
f(x)=1-\sqrt[3]{x^{2}}
integral of (2x+5)^2
\int\:(2x+5)^{2}dx
derivative of (e^x/(4x^6))
\frac{d}{dx}(\frac{e^{x}}{4x^{6}})
integral of (5x^2+7)/(x^{4/3)}
\int\:\frac{5x^{2}+7}{x^{\frac{4}{3}}}dx
integral of sin(pit)
\int\:\sin(πt)dt
(dy)/(dx)=(x-3)/(y-4)
\frac{dy}{dx}=\frac{x-3}{y-4}
(\partial)/(\partial x)((2x^3-4y)(2x^2-4))
\frac{\partial\:}{\partial\:x}((2x^{3}-4y)(2x^{2}-4))
derivative of cos(pi/2)
\frac{d}{dx}(\cos(\frac{π}{2}))
integral of 1/(x^2-2x+8)
\int\:\frac{1}{x^{2}-2x+8}dx
integral of 1/(3sqrt(x))
\int\:\frac{1}{3\sqrt{x}}dx
integral of (tan(x))^3(sec(x))^2
\int\:(\tan(x))^{3}(\sec(x))^{2}dx
derivative of 1/(x^4)
derivative\:\frac{1}{x^{4}}
derivative of x^4+5x^{-1}
\frac{d}{dx}(x^{4}+5x^{-1})
(\partial)/(\partial y)(sec^2(yt))
\frac{\partial\:}{\partial\:y}(\sec^{2}(yt))
derivative of e^{2sin(3x})
\frac{d}{dx}(e^{2\sin(3x)})
derivative of (sqrt(x+1)/(x^2-5))
\frac{d}{dx}(\frac{\sqrt{x+1}}{x^{2}-5})
f(x)=(sin(x)-cos(x))/(sin(x)+cos(x))
f(x)=\frac{\sin(x)-\cos(x)}{\sin(x)+\cos(x)}
integral of (2x-4)^2
\int\:(2x-4)^{2}dx
y^{''}+4y=x-1/20 x^2
y^{\prime\:\prime\:}+4y=x-\frac{1}{20}x^{2}
derivative of t^3-12t^2+36t
derivative\:t^{3}-12t^{2}+36t
(\partial)/(\partial x)(cos(bx+c)e^{xy}x)
\frac{\partial\:}{\partial\:x}(\cos(bx+c)e^{xy}x)
derivative of 18cos(x)+9sin^2(x)
derivative\:18\cos(x)+9\sin^{2}(x)
integral of-cos(u)
\int\:-\cos(u)du
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