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Popular Calculus Problems

(\partial)/(\partial y)(sqrt(xye^y))	\frac{\partial\:}{\partial\:y}(\sqrt{xye^{y}})
integral of (2y)/(1-y^2)	\int\:\frac{2y}{1-y^{2}}dy
derivative of g(x)=sqrt(x)e^x	derivative\:g(x)=\sqrt{x}e^{x}
integral of 4/(x^2)-7/(x^5)	\int\:\frac{4}{x^{2}}-\frac{7}{x^{5}}dx
tangent of f(x)=x^3+7x-7,(1,1)	tangent\:f(x)=x^{3}+7x-7,(1,1)
y^{''''}=0	y^{\prime\:\prime\:\prime\:\prime\:}=0
y^{''}-6y^'+25y=64e^{-t}	y^{\prime\:\prime\:}-6y^{\prime\:}+25y=64e^{-t}
integral of 2(x+2)^3	\int\:2(x+2)^{3}dx
(\partial)/(\partial x)(x^3+3xy^2-15x-12y)	\frac{\partial\:}{\partial\:x}(x^{3}+3xy^{2}-15x-12y)
(d^2y)/(dt^2)-5(dy)/(dt)-24y=0	\frac{d^{2}y}{dt^{2}}-5\frac{dy}{dt}-24y=0
limit as x approaches 0-of x-1	\lim\:_{x\to\:0-}(x-1)
integral from 0 to 1 of 3(x^2+1)e^{-x}	\int\:_{0}^{1}3(x^{2}+1)e^{-x}dx
limit as x approaches 3+of 7x^2+5	\lim\:_{x\to\:3+}(7x^{2}+5)
limit as x approaches-1 of [x]	\lim\:_{x\to\:-1}([x])
derivative of f(x)=x^3e^3sin(x)	derivative\:f(x)=x^{3}e^{3}\sin(x)
limit as x approaches-2+of sqrt(x+11)	\lim\:_{x\to\:-2+}(\sqrt{x+11})
limit as x approaches 129 of ((x-129))/(sqrt(x+15)-12)	\lim\:_{x\to\:129}(\frac{(x-129)}{\sqrt{x+15}-12})
inverse oflaplace 5/((s-1)^3)	inverselaplace\:\frac{5}{(s-1)^{3}}
integral of x 2/3	\int\:x\frac{2}{3}dx
(\partial)/(\partial x)(x^2+xln(yz))	\frac{\partial\:}{\partial\:x}(x^{2}+x\ln(yz))
limit as x approaches 0 of ln(x/(x+1))	\lim\:_{x\to\:0}(\ln(\frac{x}{x+1}))
integral of 2^{1-x}	\int\:2^{1-x}dx
sum from n=1 to infinity of n/(4^n)	\sum\:_{n=1}^{\infty\:}\frac{n}{4^{n}}
derivative of 6x-4	\frac{d}{dx}(6x-4)
y^{''}+y^'+y=xe^x+e^{-x}(1+2x)	y^{\prime\:\prime\:}+y^{\prime\:}+y=xe^{x}+e^{-x}(1+2x)
integral of (e^{-x})/(1+e^{-2x)}	\int\:\frac{e^{-x}}{1+e^{-2x}}dx
derivative of f(x)=8sin^4(sqrt(x))	derivative\:f(x)=8\sin^{4}(\sqrt{x})
derivative of 6x^5-15x^4+10x^3	\frac{d}{dx}(6x^{5}-15x^{4}+10x^{3})
(\partial)/(\partial x)(x/(y+5z))	\frac{\partial\:}{\partial\:x}(\frac{x}{y+5z})
derivative of 3^{5x+2}	\frac{d}{dx}(3^{5x+2})
taylor (-3x+28)^{5/4}	taylor\:(-3x+28)^{\frac{5}{4}}
integral from 0 to 7 of 1/(49+x^2)	\int\:_{0}^{7}\frac{1}{49+x^{2}}dx
(\partial)/(\partial x)(3y^5x^2+8yx^3)	\frac{\partial\:}{\partial\:x}(3y^{5}x^{2}+8yx^{3})
limit as x approaches 3-of (7-x-4)/(x-3)	\lim\:_{x\to\:3-}(\frac{7-x-4}{x-3})
(1+x^{14})((dy)/(dx))+14x^{13}y=11x^5	(1+x^{14})(\frac{dy}{dx})+14x^{13}y=11x^{5}
tangent of 3^{x^2-1},\at x=2	tangent\:3^{x^{2}-1},\at\:x=2
integral of 3^{5x-2}	\int\:3^{5x-2}dx
derivative of (800/x)	\frac{d}{dx}(\frac{800}{x})
limit as x approaches 4 of 2/(x-4)-(x+4)/(x^2-4x)	\lim\:_{x\to\:4}(\frac{2}{x-4}-\frac{x+4}{x^{2}-4x})
integral of (x^5-x^3+4x)/(x^4)	\int\:\frac{x^{5}-x^{3}+4x}{x^{4}}dx
integral of (sin(y))/y	\int\:\frac{\sin(y)}{y}dy
integral of sqrt(2x+7)	\int\:\sqrt{2x+7}dx
integral of (x^3)/(sqrt(4+x^2))	\int\:\frac{x^{3}}{\sqrt{4+x^{2}}}dx
normal of y=-(2x-2)^{1/3},(-3,2)	normal\:y=-(2x-2)^{\frac{1}{3}},(-3,2)
1/2 (dy)/(dx)=sqrt(y+1)cos(x)	\frac{1}{2}\frac{dy}{dx}=\sqrt{y+1}\cos(x)
derivative of y=e^{2x^2}	derivative\:y=e^{2x^{2}}
integral of (x+xe^x)	\int\:(x+xe^{x})dx
limit as x approaches 0 of (x^2+1)^{1/x}	\lim\:_{x\to\:0}((x^{2}+1)^{\frac{1}{x}})
integral of 5x^4e^{9x^5}	\int\:5x^{4}e^{9x^{5}}dx
derivative of 1/4 x^3+x-1	\frac{d}{dx}(\frac{1}{4}x^{3}+x-1)
limit as x approaches 3 of 4x^2-2x+1	\lim\:_{x\to\:3}(4x^{2}-2x+1)
slope of (-5.1)(-4.2)	slope\:(-5.1)(-4.2)
integral of 7/(x(x^4+3))	\int\:\frac{7}{x(x^{4}+3)}dx
inverse oflaplace 5/(s(s+3))	inverselaplace\:\frac{5}{s(s+3)}
integral of (cos(x))(sin(x))	\int\:(\cos(x))(\sin(x))dx
derivative of (4x^2+8x+2/(sqrt(x)))	\frac{d}{dx}(\frac{4x^{2}+8x+2}{\sqrt{x}})
x^2(dy)/(dx)+sin(x)-y=0	x^{2}\frac{dy}{dx}+\sin(x)-y=0
limit as x approaches+0 of 3x^2	\lim\:_{x\to\:+0}(3x^{2})
(dy)/(dx)=ysin(2x)	\frac{dy}{dx}=y\sin(2x)
integral of (3ax)/(b^2+c^2x^2)	\int\:\frac{3ax}{b^{2}+c^{2}x^{2}}dx
y^'=4x-y	y^{\prime\:}=4x-y
integral of s3^s	\int\:s3^{s}ds
integral of e^{-θ}cos(4θ)	\int\:e^{-θ}\cos(4θ)dθ
(\partial)/(\partial x)(2x+3)	\frac{\partial\:}{\partial\:x}(2x+3)
integral of (x^3)/((x+1)^2)	\int\:\frac{x^{3}}{(x+1)^{2}}dx
derivative of A(e^{-2x}-2e^{-2x}x)	\frac{d}{dx}(A(e^{-2x}-2e^{-2x}x))
integral of e^{2x+4}-6x	\int\:e^{2x+4}-6xdx
x^2(dy)/(dx)=(5x^2-x-3)/((x+1)(y+1))	x^{2}\frac{dy}{dx}=\frac{5x^{2}-x-3}{(x+1)(y+1)}
integral of 9x^8e^{4x^9}	\int\:9x^{8}e^{4x^{9}}dx
(\partial)/(\partial x)(x^2ln(3y-5))	\frac{\partial\:}{\partial\:x}(x^{2}\ln(3y-5))
integral of 16tan^4(xse)c^6x	\int\:16\tan^{4}(xse)c^{6}xdx
integral of sqrt(x)(x^{3/2}-4)^3	\int\:\sqrt{x}(x^{\frac{3}{2}}-4)^{3}dx
integral of sin^3(xco)s^{18}x	\int\:\sin^{3}(xco)s^{18}x
y^{''}-3y^'+2.25y=27(x^2-x)	y^{\prime\:\prime\:}-3y^{\prime\:}+2.25y=27(x^{2}-x)
integral of (6x+2)sqrt(3x^2+2x)	\int\:(6x+2)\sqrt{3x^{2}+2x}dx
derivative of 4x^3-x^4	\frac{d}{dx}(4x^{3}-x^{4})
(dy)/(dx)=k(10-y)(5-y)	\frac{dy}{dx}=k(10-y)(5-y)
integral of x^{-9}	\int\:x^{-9}dx
derivative of ((x^2+2x-3)/((x+1)^2))	\frac{d}{dx}(\frac{(x^{2}+2x-3)}{(x+1)^{2}})
tangent of f(x)=x^2+4x-1	tangent\:f(x)=x^{2}+4x-1
integral of 3x^{1/3}	\int\:3x^{\frac{1}{3}}dx
parity x-tan(x)	parity\:x-\tan(x)
limit as x approaches-4-of 2/(x^2+3x-4)	\lim\:_{x\to\:-4-}(\frac{2}{x^{2}+3x-4})
y^{''}+y^'+20y=0	y^{\prime\:\prime\:}+y^{\prime\:}+20y=0
integral from 0 to 1 of 6cos(2x)	\int\:_{0}^{1}6\cos(2x)dx
integral from 2 to 6 of 1/8 (x-2)	\int\:_{2}^{6}\frac{1}{8}(x-2)dx
derivative of 2e^{2x+1}	derivative\:2e^{2x+1}
integral of e^{x-1}	\int\:e^{x-1}dx
integral from 1 to 2 of (x-4)/(x^2)	\int\:_{1}^{2}\frac{x-4}{x^{2}}dx
integral from 0 to 1 of (5x^4-4x^3)	\int\:_{0}^{1}(5x^{4}-4x^{3})dx
tangent of g(x)=2x^2	tangent\:g(x)=2x^{2}
limit as h approaches 0 of (cos(h))/h	\lim\:_{h\to\:0}(\frac{\cos(h)}{h})
integral of (3x)/(sqrt(9+x^2))	\int\:\frac{3x}{\sqrt{9+x^{2}}}dx
derivative of f(x)=2^{2x}	derivative\:f(x)=2^{2x}
integral from 1 to 5 of 2r^2ln(r)	\int\:_{1}^{5}2r^{2}\ln(r)dr
derivative of ln(x^2+4x)	\frac{d}{dx}(\ln(x^{2}+4x))
area y=x,y=2-x,y=0	area\:y=x,y=2-x,y=0
area y=2sin(x),y=e^x,x=0,x= pi/2	area\:y=2\sin(x),y=e^{x},x=0,x=\frac{π}{2}
y^'=x^2-3y	y^{\prime\:}=x^{2}-3y
integral of (e^{-x})	\int\:(e^{-x})dx

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