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Popular Calculus Problems

x^2y^{''}-7xy^'+7y=13x^{1/2}	x^{2}y^{\prime\:\prime\:}-7xy^{\prime\:}+7y=13x^{\frac{1}{2}}
y(dy)/(dx)=3sqrt(xy^2+9x)	y\frac{dy}{dx}=3\sqrt{xy^{2}+9x}
integral of 7x^{17}e^{-x^9}	\int\:7x^{17}e^{-x^{9}}dx
(\partial)/(\partial t)(e^{st})	\frac{\partial\:}{\partial\:t}(e^{st})
derivative of axsin(x)	\frac{d}{dx}(ax\sin(x))
(dy)/(dx)=xsqrt(y)cos(x)	\frac{dy}{dx}=x\sqrt{y}\cos(x)
((dy)/(dt))-(3/t)*y=2t^3e^{2t},y(1)=0	(\frac{dy}{dt})-(\frac{3}{t})\cdot\:y=2t^{3}e^{2t},y(1)=0
derivative of f(x)=7x^2+6x	derivative\:f(x)=7x^{2}+6x
tangent of-2x^2,\at x=-2	tangent\:-2x^{2},\at\:x=-2
inverse oflaplace (12)/(s^2-5)	inverselaplace\:\frac{12}{s^{2}-5}
derivative of sqrt(1-4x)	derivative\:\sqrt{1-4x}
y^'= y/x+(y^2)/(x^2)	y^{\prime\:}=\frac{y}{x}+\frac{y^{2}}{x^{2}}
-1/2 y^'+y=4	-\frac{1}{2}y^{\prime\:}+y=4
derivative of 28x(4x^2+9)^{5/2}	derivative\:28x(4x^{2}+9)^{\frac{5}{2}}
derivative of xlog_{3}(x)	derivative\:x\log_{3}(x)
(\partial)/(\partial x)(4ycos(xy))	\frac{\partial\:}{\partial\:x}(4y\cos(xy))
derivative of xtan(x)	derivative\:x\tan(x)
integral from pi/2 to pi of sin^2(x)	\int\:_{\frac{π}{2}}^{π}\sin^{2}(x)dx
tangent of 5-4x^3	tangent\:5-4x^{3}
laplacetransform {y}	laplacetransform\:\left\{y\right\}
integral of (3x^2sqrt(16+y^2))/y	\int\:\frac{3x^{2}\sqrt{16+y^{2}}}{y}
derivative of 2/(2s^2)	derivative\:\frac{2}{2s^{2}}
simplify 3x^2+6xy-2y^2	simplify\:3x^{2}+6xy-2y^{2}
derivative of ((12x^4+e^x/(ln(x^4)))^2)	\frac{d}{dx}((\frac{12x^{4}+e^{x}}{\ln(x^{4})})^{2})
integral from-2 to 3 of (29)/(x^4)	\int\:_{-2}^{3}\frac{29}{x^{4}}dx
sum from n=1 to infinity of (n!)/(4^n)	\sum\:_{n=1}^{\infty\:}\frac{n!}{4^{n}}
integral of (sqrt(x)+1)x	\int\:(\sqrt{x}+1)xdx
derivative of (sqrt(x)/x)	\frac{d}{dx}(\frac{\sqrt{x}}{x})
(\partial)/(\partial x)(35e^{5x}y)	\frac{\partial\:}{\partial\:x}(35e^{5x}y)
integral of x^{2/7}	\int\:x^{\frac{2}{7}}dx
integral of cos(-x)	\int\:\cos(-x)dx
limit as x approaches 1 of (x-1)/(x^2-x)	\lim\:_{x\to\:1}(\frac{x-1}{x^{2}-x})
(\partial)/(\partial y)(2x^4y-1)	\frac{\partial\:}{\partial\:y}(2x^{4}y-1)
integral of (cos(x)+2cos(2x))^2	\int\:(\cos(x)+2\cos(2x))^{2}dx
tangent of f(x)=10xsin(x),\at x= pi/2	tangent\:f(x)=10x\sin(x),\at\:x=\frac{π}{2}
(\partial)/(\partial x)(1/(4-x^2))	\frac{\partial\:}{\partial\:x}(\frac{1}{4-x^{2}})
limit as x approaches 0 of (x^2)/(x^4)	\lim\:_{x\to\:0}(\frac{x^{2}}{x^{4}})
derivative of x^3-3x^2-8x+2	\frac{d}{dx}(x^{3}-3x^{2}-8x+2)
derivative of ln(((1+x)/(1-x)))	\frac{d}{dx}(\ln(\frac{(1+x)}{1-x}))
derivative of (1+sqrt(x)^2)	\frac{d}{dx}((1+\sqrt{x})^{2})
(\partial)/(\partial x)(txe^{(x^2)/(2t)})	\frac{\partial\:}{\partial\:x}(txe^{\frac{x^{2}}{2t}})
area x^4-9x^2,x^2-9	area\:x^{4}-9x^{2},x^{2}-9
derivative of 2csc(x)	derivative\:2\csc(x)
(\partial)/(\partial x)(1/2 ln(x^2+y^2))	\frac{\partial\:}{\partial\:x}(\frac{1}{2}\ln(x^{2}+y^{2}))
tangent of y=x^4+4e^x	tangent\:y=x^{4}+4e^{x}
integral of (2xsin(y)-ysin(x))	\int\:(2x\sin(y)-y\sin(x))dx
derivative of (8x^2-14xe^x)	\frac{d}{dx}((8x^{2}-14x)e^{x})
integral from 1 to 25 of e^{sqrt(x)}	\int\:_{1}^{25}e^{\sqrt{x}}dx
derivative of ln((x+3^4))	\frac{d}{dx}(\ln((x+3)^{4}))
y^{''}+4y^'-12y=0	y^{\prime\:\prime\:}+4y^{\prime\:}-12y=0
derivative of (x^2-7)sqrt(x)	derivative\:(x^{2}-7)\sqrt{x}
integral of (2x)/(\sqrt[3]{3x^2+6)}	\int\:\frac{2x}{\sqrt[3]{3x^{2}+6}}dx
derivative of (tan(x-1)/(sec(x)))	\frac{d}{dx}(\frac{\tan(x)-1}{\sec(x)})
tangent of f(x)=2sin(x),\at x= pi/3	tangent\:f(x)=2\sin(x),\at\:x=\frac{π}{3}
integral of 3/(sqrt(y))	\int\:\frac{3}{\sqrt{y}}dy
integral of (2x+3x^2)	\int\:(2x+3x^{2})dx
tangent of y=x^3-3x+1,(2,3)	tangent\:y=x^{3}-3x+1,(2,3)
integral of (int)^2	\int\:(int)^{2}dt
derivative of y=-18	derivative\:y=-18
derivative of 2sec^2(x^7)	\frac{d}{dx}(2\sec^{2}(x^{7}))
limit as x approaches 8+of sqrt(x-8)	\lim\:_{x\to\:8+}(\sqrt{x-8})
(dx)/(dt)=x^2-2x+2	\frac{dx}{dt}=x^{2}-2x+2
laplacetransform sin(2t)cos(3t)	laplacetransform\:\sin(2t)\cos(3t)
integral of 15(tan(x))(ln(cos(x)))	\int\:15(\tan(x))(\ln(\cos(x)))dx
integral of (2x)/(x^2-4)	\int\:\frac{2x}{x^{2}-4}dx
limit as x approaches 0 of ((x^2+2x))/x	\lim\:_{x\to\:0}(\frac{(x^{2}+2x)}{x})
tangent of y=4.2x-x^2	tangent\:y=4.2x-x^{2}
integral of (700x)/((x+1)^{1/3)}	\int\:\frac{700x}{(x+1)^{\frac{1}{3}}}dx
limit as x approaches 0 of (e^x-1)/(9x)	\lim\:_{x\to\:0}(\frac{e^{x}-1}{9x})
(dy)/(dx)=6x^2+3	\frac{dy}{dx}=6x^{2}+3
inverse oflaplace ((4s-5))/(s^2-6s+13)	inverselaplace\:\frac{(4s-5)}{s^{2}-6s+13}
sum from n=1 to infinity of (1/3)^n	\sum\:_{n=1}^{\infty\:}(\frac{1}{3})^{n}
area 4x^2,sqrt(x/4)	area\:4x^{2},\sqrt{\frac{x}{4}}
area y=x^2+4,y=-x^2-1,x=-2,x=3	area\:y=x^{2}+4,y=-x^{2}-1,x=-2,x=3
derivative of 30ln(2x+1)	derivative\:30\ln(2x+1)
limit as x approaches-3-of ln(x^2-9)	\lim\:_{x\to\:-3-}(\ln(x^{2}-9))
y^'+y-2sin(x)=0	y^{\prime\:}+y-2\sin(x)=0
integral from-infinity to 0 of 1/(7-2x)	\int\:_{-\infty\:}^{0}\frac{1}{7-2x}dx
derivative of 13x^3(x^2-5)	derivative\:13x^{3}(x^{2}-5)
derivative of arctan((0.9/x))	\frac{d}{dx}(\arctan(\frac{0.9}{x}))
derivative of (42)/x	derivative\:\frac{42}{x}
limit as x approaches-2 of 3x+8	\lim\:_{x\to\:-2}(3x+8)
derivative of y=e^{-x^9}	derivative\:y=e^{-x^{9}}
integral of (cos(2x))/(cos^2(x))	\int\:\frac{\cos(2x)}{\cos^{2}(x)}dx
integral of 7csc(x)cot(x)	\int\:7\csc(x)\cot(x)dx
(\partial)/(\partial x)(e^{xz+6}-cos(x+y))	\frac{\partial\:}{\partial\:x}(e^{xz+6}-\cos(x+y))
integral from 0 to 1 of [(x^2+2)-(-x)]	\int\:_{0}^{1}[(x^{2}+2)-(-x)]dx
integral of x(x-3)^7	\int\:x(x-3)^{7}dx
integral from 1 to t of (33)/(x^3)	\int\:_{1}^{t}\frac{33}{x^{3}}dx
derivative of log_{6}(2x^2+4)	\frac{d}{dx}(\log_{6}(2x^{2}+4))
integral of ((10x)/(1+5x^2))	\int\:(\frac{10x}{1+5x^{2}})dx
derivative of (2x^3)/3	derivative\:\frac{2x^{3}}{3}
derivative of (e^x/(3x^2))	\frac{d}{dx}(\frac{e^{x}}{3x^{2}})
limit as x approaches 0 of 6x^2(cot(3x))(csc(2x))	\lim\:_{x\to\:0}(6x^{2}(\cot(3x))(\csc(2x)))
integral from 0 to 1 of (sqrt(x)-x^2)^2	\int\:_{0}^{1}(\sqrt{x}-x^{2})^{2}dx
integral of (x-1)/(sqrt(x^2-4x+3))	\int\:\frac{x-1}{\sqrt{x^{2}-4x+3}}dx
sum from n=0 to infinity of n/(n+1)x^n	\sum\:_{n=0}^{\infty\:}\frac{n}{n+1}x^{n}
derivative of 5e^{-2x}	\frac{d}{dx}(5e^{-2x})
integral of-4cos^2(x)	\int\:-4\cos^{2}(x)dx
derivative of (x-1(x+2))	\frac{d}{dx}((x-1)(x+2))

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