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Popular Calculus Problems

derivative of (2x+6x^2/((1+6x)^2))	\frac{d}{dx}(\frac{2x+6x^{2}}{(1+6x)^{2}})
y+sqrt(x^2+y^2)dx-xdy=0	y+\sqrt{x^{2}+y^{2}}dx-xdy=0
y^{''}-3y^'-4y=0,y(0)=a,y^'(0)=-20	y^{\prime\:\prime\:}-3y^{\prime\:}-4y=0,y(0)=a,y^{\prime\:}(0)=-20
derivative of x^{8/3}-20x^{2/3}	\frac{d}{dx}(x^{\frac{8}{3}}-20x^{\frac{2}{3}})
(dy)/(dx)=y^2sin(x^2),y(-2)= 1/3	\frac{dy}{dx}=y^{2}\sin(x^{2}),y(-2)=\frac{1}{3}
f(r)=pir^2	f(r)=πr^{2}
tangent of 2xsqrt(x),\at x=1	tangent\:2x\sqrt{x},\at\:x=1
derivative of 6sqrt(x)	derivative\:6\sqrt{x}
integral of (2xy-tan(y))	\int\:(2xy-\tan(y))dx
derivative of 9e^{-x}+e^{2x}	\frac{d}{dx}(9e^{-x}+e^{2x})
area y=cos(x),y=2-cos(x)	area\:y=\cos(x),y=2-\cos(x)
derivative of 3sqrt(x)+2	\frac{d}{dx}(3\sqrt{x}+2)
integral of 2-2cos(x)	\int\:2-2\cos(x)dx
tangent of 1/3 x^3-4x^2+17x+13	tangent\:\frac{1}{3}x^{3}-4x^{2}+17x+13
integral of 5e^{8-4x}-5	\int\:5e^{8-4x}-5dx
(\partial)/(\partial x)(\|Ax\|^2)	\frac{\partial\:}{\partial\:x}(\left\|Ax\right\|^{2})
derivative of f(x)=e^{-3.5x^2}	derivative\:f(x)=e^{-3.5x^{2}}
integral of 1/(n^2)	\int\:\frac{1}{n^{2}}
derivative of (x^2-1^5)	\frac{d}{dx}((x^{2}-1)^{5})
y^{''}-289y=0	y^{\prime\:\prime\:}-289y=0
derivative of 2cos(sin(x))	\frac{d}{dx}(2\cos(\sin(x)))
slope of y=2x^2+3/x	slope\:y=2x^{2}+\frac{3}{x}
integral of 4sin^3(6x)cos^3(6x)	\int\:4\sin^{3}(6x)\cos^{3}(6x)dx
integral of (-2xy)/((x^2+y^2)^2)	\int\:\frac{-2xy}{(x^{2}+y^{2})^{2}}dy
limit as x approaches-3 of 3x+2	\lim\:_{x\to\:-3}(3x+2)
(\partial)/(\partial x)(ycos(x)+sin(x))	\frac{\partial\:}{\partial\:x}(y\cos(x)+\sin(x))
integral of x^2(6-x^3)^5	\int\:x^{2}(6-x^{3})^{5}dx
slope of (-3)(1.2)	slope\:(-3)(1.2)
derivative of 1/y+xln(y)	\frac{d}{dx}(\frac{1}{y}+x\ln(y))
integral of ln(x)*x	\int\:\ln(x)\cdot\:xdx
tangent of f(x)=2xsqrt(3-4x),\at x=-1	tangent\:f(x)=2x\sqrt{3-4x},\at\:x=-1
integral of-5x^{-1}	\int\:-5x^{-1}dx
integral from-infinity to 4 of 1/(x^2+1)	\int\:_{-\infty\:}^{4}\frac{1}{x^{2}+1}dx
simplify ((3x^2-2)/(2x+3))^3	simplify\:(\frac{3x^{2}-2}{2x+3})^{3}
integral of (5x^2+6x-8)	\int\:(5x^{2}+6x-8)dx
integral of ((x^4+8))/(x^3)	\int\:\frac{(x^{4}+8)}{x^{3}}dx
taylor 8/(sqrt(x))	taylor\:\frac{8}{\sqrt{x}}
integral of tan(9xse)c^29x	\int\:\tan(9xse)c^{2}9xdx
(dy)/(dx)=((x-1))/(y-3)	\frac{dy}{dx}=\frac{(x-1)}{y-3}
integral of 1/(4-5x)	\int\:\frac{1}{4-5x}dx
(\partial)/(\partial x)(sqrt(x^3))	\frac{\partial\:}{\partial\:x}(\sqrt{x^{3}})
(\partial)/(\partial x)((3x^2+5x+1)*(y+4))	\frac{\partial\:}{\partial\:x}((3x^{2}+5x+1)\cdot\:(y+4))
(dy)/(dx)=y(xy^3-1)	\frac{dy}{dx}=y(xy^{3}-1)
derivative of arccsc(sqrt((x+1/(1-x))))	\frac{d}{dx}(\arccsc(\sqrt{\frac{x+1}{1-x}}))
y^{''}+4y^'+5y=35e-4x,y(0)=-5,y^'(0)=1	y^{\prime\:\prime\:}+4y^{\prime\:}+5y=35e-4x,y(0)=-5,y^{\prime\:}(0)=1
integral of sqrt(11-10x-x^2)	\int\:\sqrt{11-10x-x^{2}}dx
integral of 2/((1+x^2))-4/x	\int\:\frac{2}{(1+x^{2})}-\frac{4}{x}dx
derivative of f(x)=3x^5+2x^2	derivative\:f(x)=3x^{5}+2x^{2}
integral of (4x^3-3x^2)(4x^4-4x^3)^5	\int\:(4x^{3}-3x^{2})(4x^{4}-4x^{3})^{5}dx
integral from-2 to 0 of x^3-x^2-6x	\int\:_{-2}^{0}x^{3}-x^{2}-6xdx
(\partial)/(\partial x)(t^{-3}(x^2)/(2t))	\frac{\partial\:}{\partial\:x}(t^{-3}\frac{x^{2}}{2t})
integral of x^{-5/3}	\int\:x^{-\frac{5}{3}}dx
integral of (10/9 x+14)/(x^2+9)	\int\:\frac{\frac{10}{9}x+14}{x^{2}+9}dx
integral of (sinh(ln(x)))/x	\int\:\frac{\sinh(\ln(x))}{x}dx
limit as x approaches+0 of (\|x-3\|)/(x-3)	\lim\:_{x\to\:+0}(\frac{\left\|x-3\right\|}{x-3})
integral of (y^2+28y+196)/((y^2+196)^2)	\int\:\frac{y^{2}+28y+196}{(y^{2}+196)^{2}}dy
limit as x approaches-4 of (x^2-1)/(4-x)	\lim\:_{x\to\:-4}(\frac{x^{2}-1}{4-x})
integral from 0 to 1 of cos((pix)/2)	\int\:_{0}^{1}\cos(\frac{πx}{2})dx
y^{''}+4y^'=(4t-4)sin(3t)	y^{\prime\:\prime\:}+4y^{\prime\:}=(4t-4)\sin(3t)
sum from n=0 to infinity of 0.8^n	\sum\:_{n=0}^{\infty\:}0.8^{n}
derivative of e^x(x+xsqrt(x))	derivative\:e^{x}(x+x\sqrt{x})
derivative of ln((5x^2+x+6/(x^3)))	\frac{d}{dx}(\ln(\frac{5x^{2}+x+6}{x^{3}}))
integral from 0 to 1 of 12e^{3x}	\int\:_{0}^{1}12e^{3x}dx
inverse oflaplace s/(s^2+23pi*s+pi^2)	inverselaplace\:\frac{s}{s^{2}+2\cdot\:3\cdot\:π\cdot\:s+π^{2}}
derivative of (5x+e^x(5-sqrt(x)))	\frac{d}{dx}((5x+e^{x})(5-\sqrt{x}))
d/(dt)(2e^{2t})	\frac{d}{dt}(2e^{2t})
integral of 4x(x^2+29000)^{-2/3}	\int\:4x(x^{2}+29000)^{-\frac{2}{3}}dx
limit as x approaches 2+of x-2	\lim\:_{x\to\:2+}(x-2)
derivative of ln(1+a/x)	\frac{d}{dx}(\ln(1+\frac{a}{x}))
limit as x approaches+3 of f(x)	\lim\:_{x\to\:+3}(f(x))
inverse oflaplace 1/(s(s+2))	inverselaplace\:\frac{1}{s(s+2)}
integral of 13(tan(x))(ln(cos(x)))	\int\:13(\tan(x))(\ln(\cos(x)))dx
limit as x approaches+pi/2 of cot(x)	\lim\:_{x\to\:+\frac{π}{2}}(\cot(x))
derivative of f(x)=5arcsin(x^3)	derivative\:f(x)=5\arcsin(x^{3})
derivative of (e^x)/x	derivative\:\frac{e^{x}}{x}
integral from 1 to 2 of xln(x)	\int\:_{1}^{2}x\ln(x)dx
x(dy)/(dx)+(2x+1)y=xe^{-2x}	x\frac{dy}{dx}+(2x+1)y=xe^{-2x}
integral of (x^2)/(x-2)	\int\:\frac{x^{2}}{x-2}dx
integral of (e^x+1)^3e^x	\int\:(e^{x}+1)^{3}e^{x}dx
integral of e^{i8x}cos(5x)	\int\:e^{i8x}\cos(5x)dx
limit as x approaches 0+of xcot(x)csc(x)	\lim\:_{x\to\:0+}(x\cot(x)\csc(x))
tangent of x^4,\at x=3	tangent\:x^{4},\at\:x=3
derivative of (16/((1+2x)^3))	\frac{d}{dx}(\frac{16}{(1+2x)^{3}})
derivative of arctan(cos(3x))	derivative\:\arctan(\cos(3x))
integral of (x-1)/(x^3)	\int\:\frac{x-1}{x^{3}}dx
f(y)=2e^y	f(y)=2e^{y}
limit as x approaches-4 of (4/x+1)/(x+4)	\lim\:_{x\to\:-4}(\frac{\frac{4}{x}+1}{x+4})
integral from 0 to 1 of sqrt(1+(-2x)^2)	\int\:_{0}^{1}\sqrt{1+(-2x)^{2}}dx
tangent of f(x)=x^2+5,(3,14)	tangent\:f(x)=x^{2}+5,(3,14)
derivative of x/4-4/x	derivative\:\frac{x}{4}-\frac{4}{x}
x^2(dy)/(dx)-2xy=6y^4,y(1)= 1/3	x^{2}\frac{dy}{dx}-2xy=6y^{4},y(1)=\frac{1}{3}
limit as x approaches infinity of 7x	\lim\:_{x\to\:\infty\:}(7x)
integral of 1/(x+7)	\int\:\frac{1}{x+7}dx
integral from 4 to 5 of x/8	\int\:_{4}^{5}\frac{x}{8}dx
integral of ln(a+bx)	\int\:\ln(a+bx)dx
inverse oflaplace 1/((s-1)^2-4)	inverselaplace\:\frac{1}{(s-1)^{2}-4}
(x^2+2)y^'+2xy=x^3	(x^{2}+2)y^{\prime\:}+2xy=x^{3}
integral from 0 to 5 of 4x^2	\int\:_{0}^{5}4x^{2}dx
integral of 2z^2	\int\:2z^{2}dz
integral of 1/(3-6x-x^2)	\int\:\frac{1}{3-6x-x^{2}}dx

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