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Popular Calculus Problems

limit as x approaches 2 of sqrt(x-2)	\lim\:_{x\to\:2}(\sqrt{x-2})
integral of 1/(x*(1-x))	\int\:\frac{1}{x\cdot\:(1-x)}dx
derivative of f(x)=sqrt(x+5)	derivative\:f(x)=\sqrt{x+5}
taylor sin(2x),pi	taylor\:\sin(2x),π
integral from 0 to pi of x*sin(2x)	\int\:_{0}^{π}x\cdot\:\sin(2x)dx
(dy)/(dx)=(x-2)e^{-2y},y(2)=ln(2)	\frac{dy}{dx}=(x-2)e^{-2y},y(2)=\ln(2)
integral from 0 to pi/3 of sin(3x)	\int\:_{0}^{\frac{π}{3}}\sin(3x)dx
integral from-4 to 4 of sqrt(90)	\int\:_{-4}^{4}\sqrt{90}dt
limit as x approaches 0 of 5/(x^8)	\lim\:_{x\to\:0}(\frac{5}{x^{8}})
(\partial)/(\partial x)(e^{3x}cos(6y))	\frac{\partial\:}{\partial\:x}(e^{3x}\cos(6y))
(dx)/(dt)=2+x/(20)	\frac{dx}{dt}=2+\frac{x}{20}
derivative of y=5x-15	derivative\:y=5x-15
derivative of-3/(16(1+x^{7/4)})	\frac{d}{dx}(-\frac{3}{16(1+x)^{\frac{7}{4}}})
integral of 4e^xsqrt(4+e^x)	\int\:4e^{x}\sqrt{4+e^{x}}dx
derivative of (2x+1^6)	\frac{d}{dx}((2x+1)^{6})
integral from-1 to 2 of (x^2-3x)	\int\:_{-1}^{2}(x^{2}-3x)dx
(dx}{dy}=\frac{x^2y+y^3)/x	\frac{dx}{dy}=\frac{x^{2}y+y^{3}}{x}
(\partial)/(\partial x)(cos^3(x^8y^8))	\frac{\partial\:}{\partial\:x}(\cos^{3}(x^{8}y^{8}))
derivative of 1/(x*ln(x))	\frac{d}{dx}(\frac{1}{x\cdot\:\ln(x)})
limit as x approaches-2+of-6	\lim\:_{x\to\:-2+}(-6)
solvefor f,tan(f)(x)=(sqrt(x)+1)/(sqrt(x^3))	solvefor\:f,\tan(f)(x)=\frac{\sqrt{x}+1}{\sqrt{x^{3}}}
implicit 3x^2+xy+3y^2=7	implicit\:3x^{2}+xy+3y^{2}=7
integral of cos(2x+y)	\int\:\cos(2x+y)dx
integral from 1 to 2 of 8x^3+3x^2	\int\:_{1}^{2}8x^{3}+3x^{2}dx
integral of cos^{(5)}(2x)	\int\:\cos^{(5)}(2x)dx
(\partial)/(\partial x)(1+e^{2x})	\frac{\partial\:}{\partial\:x}(1+e^{2x})
integral from-1 to 3 of (t+2)(t^2-2t+4)	\int\:_{-1}^{3}(t+2)(t^{2}-2t+4)dt
taylor e^{-x},0.25	taylor\:e^{-x},0.25
(\partial)/(\partial x)(x^2+y^2-2x-2y)	\frac{\partial\:}{\partial\:x}(x^{2}+y^{2}-2x-2y)
derivative of (x^2-4/(x^2))	\frac{d}{dx}(\frac{x^{2}-4}{x^{2}})
tangent of f(x)=e^{4x},\at x= 1/4 ln(5)	tangent\:f(x)=e^{4x},\at\:x=\frac{1}{4}\ln(5)
area f(x)=2sin(x)+sin(2x),y=0,0<= x<= pi	area\:f(x)=2\sin(x)+\sin(2x),y=0,0\le\:x\le\:π
x^'=x-15	x^{\prime\:}=x-15
derivative of 2/((2+x^3))	\frac{d}{dx}(\frac{2}{(2+x)^{3}})
(d^3)/(dx^3)(4/x)	\frac{d^{3}}{dx^{3}}(\frac{4}{x})
(\partial)/(\partial y)(e^{2x}sin(y))	\frac{\partial\:}{\partial\:y}(e^{2x}\sin(y))
derivative of-4+2e^x-3x	derivative\:-4+2e^{x}-3x
integral of xsqrt(x^2+2)	\int\:x\sqrt{x^{2}+2}dx
tangent of f(x)=-x^3+3x^2	tangent\:f(x)=-x^{3}+3x^{2}
derivative of f(x)= 4/((x^2+1)^2)	derivative\:f(x)=\frac{4}{(x^{2}+1)^{2}}
derivative of 6x-9	\frac{d}{dx}(6x-9)
y^{'''}-9y^{''}+20y^'=0	y^{\prime\:\prime\:\prime\:}-9y^{\prime\:\prime\:}+20y^{\prime\:}=0
(\partial)/(\partial x)(((x+y))/(xy-1))	\frac{\partial\:}{\partial\:x}(\frac{(x+y)}{xy-1})
integral from 15 to 30 of 9	\int\:_{15}^{30}9dx
derivative of x/(sqrt(x^2+36))	\frac{d}{dx}(\frac{x}{\sqrt{x^{2}+36}})
integral from-1 to 2 of (9-x^2)-(x+1)	\int\:_{-1}^{2}(9-x^{2})-(x+1)dx
derivative of x^{n+1}	\frac{d}{dx}(x^{n+1})
derivative of ((x-1)/x)	\frac{d}{dx}(\frac{(x-1)}{x})
(\partial)/(\partial x)(x^3-3xy)	\frac{\partial\:}{\partial\:x}(x^{3}-3xy)
(\partial)/(\partial y)(3x+5y-1)	\frac{\partial\:}{\partial\:y}(3x+5y-1)
derivative of ln(x^2sqrt(x^2+1))	\frac{d}{dx}(\ln(x^{2}\sqrt{x^{2}+1}))
(dy}{dx}=\frac{(6xsec(y/x)+y))/x	\frac{dy}{dx}=\frac{(6x\sec(\frac{y}{x})+y)}{x}
taylor cos(x)+1/x , pi/2	taylor\:\cos(x)+\frac{1}{x},\frac{π}{2}
tangent of f(x)=sqrt(x^2+18x+86),\at x=0	tangent\:f(x)=\sqrt{x^{2}+18x+86},\at\:x=0
integral of-1/2 e^{-2x}	\int\:-\frac{1}{2}e^{-2x}dx
integral from 0 to x of 1/(1+t^2)	\int\:_{0}^{x}\frac{1}{1+t^{2}}dt
(\partial)/(\partial x)((xe^{x+2y})(1+2y))	\frac{\partial\:}{\partial\:x}((xe^{x+2y})(1+2y))
integral of (-x^3-x^2-4x+28)/(x^3+4x)	\int\:\frac{-x^{3}-x^{2}-4x+28}{x^{3}+4x}dx
(\partial)/(\partial x)(\sqrt[4]{4x^2+2})	\frac{\partial\:}{\partial\:x}(\sqrt[4]{4x^{2}+2})
integral from 0 to 7 of 8/(9x^2+10x+1)	\int\:_{0}^{7}\frac{8}{9x^{2}+10x+1}dx
(\partial)/(\partial x)(e^{3y}cos(-3x))	\frac{\partial\:}{\partial\:x}(e^{3y}\cos(-3x))
area y=e^x,y=9-e^x,x=-1,x=1	area\:y=e^{x},y=9-e^{x},x=-1,x=1
derivative of (sin(ln(t)))^2	derivative\:(\sin(\ln(t)))^{2}
y^'=4y(1-y/4)	y^{\prime\:}=4y(1-\frac{y}{4})
limit as x approaches 0 of-4/(x^2)	\lim\:_{x\to\:0}(-\frac{4}{x^{2}})
derivative of (x^3-5x^2+1)/(x^2)	derivative\:\frac{x^{3}-5x^{2}+1}{x^{2}}
integral from 0 to 1/2 of 5arcsin(2y)	\int\:_{0}^{\frac{1}{2}}5\arcsin(2y)dy
integral of 1/(x^2sqrt(x^2-100))	\int\:\frac{1}{x^{2}\sqrt{x^{2}-100}}dx
derivative of f(x)=(sec(x))/(8+sec(x))	derivative\:f(x)=\frac{\sec(x)}{8+\sec(x)}
integral of 1/(x^3sqrt(x^2-100))	\int\:\frac{1}{x^{3}\sqrt{x^{2}-100}}dx
derivative of 3x^3e^{-x}	\frac{d}{dx}(3x^{3}e^{-x})
derivative of f(x)=3xe^{2x}	derivative\:f(x)=3xe^{2x}
d/(dt)(1/(sqrt(1+t^2)))	\frac{d}{dt}(\frac{1}{\sqrt{1+t^{2}}})
limit as x approaches 3 of 5^x	\lim\:_{x\to\:3}(5^{x})
limit as x approaches 2-of (x^2)/(4-x^2)	\lim\:_{x\to\:2-}(\frac{x^{2}}{4-x^{2}})
derivative of-4x-(676)/x	derivative\:-4x-\frac{676}{x}
integral of xsqrt(36+x^2)	\int\:x\sqrt{36+x^{2}}dx
integral of x/((x-1)^2)	\int\:\frac{x}{(x-1)^{2}}dx
integral of (1/x-5/(9x^2+1))	\int\:(\frac{1}{x}-\frac{5}{9x^{2}+1})dx
derivative of 3x^2y	\frac{d}{dx}(3x^{2}y)
limit as x approaches 2 of x^3+2x^2-x-4	\lim\:_{x\to\:2}(x^{3}+2x^{2}-x-4)
derivative of (3x^2+5(3x-1)^2)	\frac{d}{dx}((3x^{2}+5)(3x-1)^{2})
derivative of 2x^2e^x	derivative\:2x^{2}e^{x}
derivative of f(x)= 3/(4x^5)	derivative\:f(x)=\frac{3}{4x^{5}}
derivative of 4x^8+3e^{7x}	\frac{d}{dx}(4x^{8}+3e^{7x})
derivative of \sqrt[8]{x}-9/x	\frac{d}{dx}(\sqrt[8]{x}-\frac{9}{x})
limit as x approaches 3 of x^2+x	\lim\:_{x\to\:3}(x^{2}+x)
y=ln(x^2+5)	y=\ln(x^{2}+5)
sum from n=1 to infinity of 1/(4n-2)	\sum\:_{n=1}^{\infty\:}\frac{1}{4n-2}
(\partial)/(\partial x)(x^2+2y^2+3z^2-1)	\frac{\partial\:}{\partial\:x}(x^{2}+2y^{2}+3z^{2}-1)
integral of 7ln(x^2-1)	\int\:7\ln(x^{2}-1)dx
(\partial)/(\partial z)(xe^y+ye^z+ze^x)	\frac{\partial\:}{\partial\:z}(xe^{y}+ye^{z}+ze^{x})
integral of (1-x^2)^{0.5}	\int\:(1-x^{2})^{0.5}dx
tangent of 2/(4-x),\at x=1	tangent\:\frac{2}{4-x},\at\:x=1
integral of sin^2(4x)cos^2(x)4x	\int\:\sin^{2}(4x)\cos^{2}(x)4xdx
(dy)/(dx)=5xe^y,y(0)=0	\frac{dy}{dx}=5xe^{y},y(0)=0
integral of (x^3)/(3-x^4)	\int\:\frac{x^{3}}{3-x^{4}}dx
derivative of 12sqrt(x)tanh(sqrt(x))	\frac{d}{dx}(12\sqrt{x}\tanh(\sqrt{x}))
tangent of y=x^4-5x^3+2,\at x=2	tangent\:y=x^{4}-5x^{3}+2,\at\:x=2
(\partial)/(\partial y)(4-x^2-y^2)	\frac{\partial\:}{\partial\:y}(4-x^{2}-y^{2})

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