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Popular Calculus Problems

(\partial}{\partial x}(e^{-(\frac{x^2+y^2)/2)})	\frac{\partial\:}{\partial\:x}(e^{-(\frac{x^{2}+y^{2}}{2})})
integral from 2 to 6 of x/(x^2+6x+13)	\int\:_{2}^{6}\frac{x}{x^{2}+6x+13}dx
integral of-1/(x^2+1)	\int\:-\frac{1}{x^{2}+1}dx
area y=x^7,-2,3	area\:y=x^{7},-2,3
limit as t approaches 0 of 8/t-8/(t^2+t)	\lim\:_{t\to\:0}(\frac{8}{t}-\frac{8}{t^{2}+t})
derivative of tan(y)	derivative\:\tan(y)
y^'=(9x)/(y+x^2y),y(0)=-5	y^{\prime\:}=\frac{9x}{y+x^{2}y},y(0)=-5
limit as x approaches 0 of 7sin(1/x)	\lim\:_{x\to\:0}(7\sin(\frac{1}{x}))
limit as x approaches infinity of 1/10	\lim\:_{x\to\:\infty\:}(\frac{1}{10})
integral of e^{7x+3}	\int\:e^{7x+3}dx
integral of 1/(4e^x)	\int\:\frac{1}{4e^{x}}dx
integral of 19sec^{-2}(xta)n^3x	\int\:19\sec^{-2}(xta)n^{3}xdx
y^'+6y=1,y(0)=1	y^{\prime\:}+6y=1,y(0)=1
implicit x^2+xy-y^2=4	implicit\:x^{2}+xy-y^{2}=4
16y^{''}+72y^'+87y=0,y(0)=2,y^'(0)=4	16y^{\prime\:\prime\:}+72y^{\prime\:}+87y=0,y(0)=2,y^{\prime\:}(0)=4
(dv)/(dx)-8v=10	\frac{dv}{dx}-8v=10
(dy)/(dx)(3)+(xy+5x)=0	\frac{dy}{dx}(3)+(xy+5x)=0
integral of ((ln(x))^{18})/x	\int\:\frac{(\ln(x))^{18}}{x}dx
integral of 4xe^{2x}	\int\:4xe^{2x}dx
integral from 0 to 2pi of tsin(2t)	\int\:_{0}^{2π}t\sin(2t)dt
f(x)=(2x-6)^4(x^2+x+1)^5	f(x)=(2x-6)^{4}(x^{2}+x+1)^{5}
derivative of ((x-1)/(x^2))	\frac{d}{dx}(\frac{(x-1)}{x^{2}})
derivative of 2x^2-x^3	\frac{d}{dx}(2x^{2}-x^{3})
integral of (x^2-5)^20.2x	\int\:(x^{2}-5)^{2}0.2xdx
integral from 6 to 7 of x/(x-6)	\int\:_{6}^{7}\frac{x}{x-6}dx
integral of (3x+2)	\int\:(3x+2)dx
integral of-1e^x	\int\:-1e^{x}dx
integral of (x^3)/3+2x-5	\int\:\frac{x^{3}}{3}+2x-5dx
limit as x approaches 3-of 2x^3	\lim\:_{x\to\:3-}(2x^{3})
(\partial)/(\partial x)(sin(cx))	\frac{\partial\:}{\partial\:x}(\sin(cx))
derivative of (x^3/3-5x^2+21x+1)	\frac{d}{dx}(\frac{x^{3}}{3}-5x^{2}+21x+1)
limit as x approaches 3 of-6	\lim\:_{x\to\:3}(-6)
limit as x approaches 9-of 3/(x-9)	\lim\:_{x\to\:9-}(\frac{3}{x-9})
integral of x/(x^2+a^2)	\int\:\frac{x}{x^{2}+a^{2}}dx
derivative of f(x)=sqrt(9-x^2)	derivative\:f(x)=\sqrt{9-x^{2}}
derivative of y=x^2ln(4x+3)	derivative\:y=x^{2}\ln(4x+3)
derivative of (x^2^x)	\frac{d}{dx}((x^{2})^{x})
integral of (2y)	\int\:(2y)dy
integral of ((5x-7))/((x^2-x-2)(x-3))	\int\:\frac{(5x-7)}{(x^{2}-x-2)(x-3)}dx
y^'+xy=-x^2	y^{\prime\:}+xy=-x^{2}
derivative of y=(5x-4)^5(3-x^3)^5	derivative\:y=(5x-4)^{5}(3-x^{3})^{5}
tangent of f(x)=2x^2-6x,\at x=1	tangent\:f(x)=2x^{2}-6x,\at\:x=1
tangent of g(x)=sqrt(5x+20),\at x=1	tangent\:g(x)=\sqrt{5x+20},\at\:x=1
derivative of sqrt(4x+3)	derivative\:\sqrt{4x+3}
y^{''}-6y^'+9y=e^{3x}	y^{\prime\:\prime\:}-6y^{\prime\:}+9y=e^{3x}
limit as x approaches 3 of xsqrt(25-x^3)	\lim\:_{x\to\:3}(x\sqrt{25-x^{3}})
derivative of 3-2sin(2x-pi/4)	\frac{d}{dx}(3-2\sin(2x-\frac{π}{4}))
integral of e^x3x^2	\int\:e^{x}3x^{2}dx
x^2(d^2y)/(dx^2)-5x(dy)/(dx)+9y=0	x^{2}\frac{d^{2}y}{dx^{2}}-5x\frac{dy}{dx}+9y=0
integral of ((x^2-x+30))/(x^3+5x)	\int\:\frac{(x^{2}-x+30)}{x^{3}+5x}dx
derivative of \sqrt[3]{x}+6sqrt(x^3)	derivative\:\sqrt[3]{x}+6\sqrt{x^{3}}
derivative of 2^{x+1}	\frac{d}{dx}(2^{x+1})
integral of e^xsqrt(e^{2x)+4}	\int\:e^{x}\sqrt{e^{2x}+4}dx
integral of cos^4(x)*sin^3(x)	\int\:\cos^{4}(x)\cdot\:\sin^{3}(x)dx
derivative of x^2+sin(2x)	\frac{d}{dx}(x^{2}+\sin(2x))
derivative of (3(2x+1)/(sqrt(6x+6x^2)))	\frac{d}{dx}(\frac{3(2x+1)}{\sqrt{6x+6x^{2}}})
(dy)/(dx)=sin(3y)ln(x)	\frac{dy}{dx}=\sin(3y)\ln(x)
derivative of sin(x)+7/2 cot(x)	derivative\:\sin(x)+\frac{7}{2}\cot(x)
integral of ye^{-xy}	\int\:ye^{-xy}dx
derivative of f(x)=(x-2)/(x^2)	derivative\:f(x)=\frac{x-2}{x^{2}}
integral from 0 to a of xsqrt(a^2-x^2)	\int\:_{0}^{a}x\sqrt{a^{2}-x^{2}}dx
limit as x approaches 3 of 5/(x-3)	\lim\:_{x\to\:3}(\frac{5}{x-3})
integral from 0 to 2 of (2x)/(x^2-4)	\int\:_{0}^{2}\frac{2x}{x^{2}-4}dx
integral of 9+12cos(x)+4cos^2(x)	\int\:9+12\cos(x)+4\cos^{2}(x)dx
taylor sqrt(x)4	taylor\:\sqrt{x}4
f^'(x)=1.9181x^2+177.69x-0.4*x^3	f^{\prime\:}(x)=1.9181\cdot\:x^{2}+177.69\cdot\:x-0.4\cdot\:x^{3}
derivative of (8-9x)(8+9x)	derivative\:(8-9x)(8+9x)
derivative of (1-x/2)^{e^{x^2}}	derivative\:(1-\frac{x}{2})^{e^{x^{2}}}
sum from n=1 to infinity of 4/(n^3)	\sum\:_{n=1}^{\infty\:}\frac{4}{n^{3}}
y^{''}+36y=-2tan(6x)	y^{\prime\:\prime\:}+36y=-2\tan(6x)
derivative of ((sin(x)/(cos(2x)))^3)	\frac{d}{dx}((\frac{\sin(x)}{\cos(2x)})^{3})
f^'(x)=3cos(x)+4(-sin(x))	f^{\prime\:}(x)=3\cos(x)+4(-\sin(x))
limit as x approaches 0+of 2/(ln(x))	\lim\:_{x\to\:0+}(\frac{2}{\ln(x)})
derivative of 8x^2ln(8x)	\frac{d}{dx}(8x^{2}\ln(8x))
inverse oflaplace 1/(s^4+1)	inverselaplace\:\frac{1}{s^{4}+1}
integral from 0 to pi/2 of cos(2x)	\int\:_{0}^{\frac{π}{2}}\cos(2x)dx
derivative of 1/4 cos(x/4)	\frac{d}{dx}(\frac{1}{4}\cos(\frac{x}{4}))
derivative of-x+2	derivative\:-x+2
integral of (e^x)/(sqrt(1-9e^{2x))}	\int\:\frac{e^{x}}{\sqrt{1-9e^{2x}}}dx
integral of 1/(4x^2+7)	\int\:\frac{1}{4x^{2}+7}dx
limit as (x,y) approaches (0,0) of (2x)/(x^2+x+y^2)	\lim\:_{(x,y)\to\:(0,0)}(\frac{2x}{x^{2}+x+y^{2}})
integral of (3x+5)/(x^3-x^2-x+1)	\int\:\frac{3x+5}{x^{3}-x^{2}-x+1}dx
derivative of arctan(sin(x^2+pi/x))	\frac{d}{dx}(\arctan(\sin(x^{2}+\frac{π}{x})))
y^{''}+y^'+y=t	y^{\prime\:\prime\:}+y^{\prime\:}+y=t
derivative of 6x^2-4x	\frac{d}{dx}(6x^{2}-4x)
y^{''}+5y=0,y^'(1)=5	y^{\prime\:\prime\:}+5y=0,y^{\prime\:}(1)=5
derivative of-1/(4x^{3/2)}	derivative\:-\frac{1}{4x^{\frac{3}{2}}}
y^{''}+8y^'+20y=0	y^{\prime\:\prime\:}+8y^{\prime\:}+20y=0
derivative of x^{1/4}cos(sqrt(7)ln(x))	\frac{d}{dx}(x^{\frac{1}{4}}\cos(\sqrt{7}\ln(x)))
(\partial)/(\partial x)(x/(y^2)sin(x/y))	\frac{\partial\:}{\partial\:x}(\frac{x}{y^{2}}\sin(\frac{x}{y}))
integral from 1 to 4 of 7sqrt(t)ln(t)	\int\:_{1}^{4}7\sqrt{t}\ln(t)dt
derivative of y=(7ln(x))^2	derivative\:y=(7\ln(x))^{2}
(\partial)/(\partial x)(x^e)	\frac{\partial\:}{\partial\:x}(x^{e})
integral from-infinity to 0 of ze^{9z}	\int\:_{-\infty\:}^{0}ze^{9z}dz
integral of x/((x+t)^2)	\int\:\frac{x}{(x+t)^{2}}
derivative of 4arcsin((2x-4/(3x+2)))	\frac{d}{dx}(4\arcsin(\frac{2x-4}{3x+2}))
limit as x approaches 1 of (3-3/x)/(x-1)	\lim\:_{x\to\:1}(\frac{3-\frac{3}{x}}{x-1})
derivative of e^{20}	derivative\:e^{20}
tangent of y=(12x)/(x^2-4),(4,4)	tangent\:y=\frac{12x}{x^{2}-4},(4,4)
simplify (x+2xt+cos(t))/(1+t^2)	simplify\:\frac{x+2xt+\cos(t)}{1+t^{2}}

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