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Popular Calculus Problems

(d^2y)/(dx^2)=4y,y(0)=0,y^'(0)=1	\frac{d^{2}y}{dx^{2}}=4y,y(0)=0,y^{\prime\:}(0)=1
y^{''}-y^'=xe^x	y^{\prime\:\prime\:}-y^{\prime\:}=xe^{x}
12= 1/((22*10^{-6))}y+(33000dy)/(dx)	12=\frac{1}{(22\cdot\:10^{-6})}y+\frac{33000dy}{dx}
(\partial)/(\partial x)(ln(y)+4x)	\frac{\partial\:}{\partial\:x}(\ln(y)+4x)
limit as x approaches-3 of (16-x^{4/3})/(4-x^{2/3)}	\lim\:_{x\to\:-3}(\frac{16-x^{\frac{4}{3}}}{4-x^{\frac{2}{3}}})
limit as x approaches 3-of 1/(3-x)	\lim\:_{x\to\:3-}(\frac{1}{3-x})
integral of ke^{3x}	\int\:ke^{3x}dx
derivative of sqrt(x)+5sin(x)	\frac{d}{dx}(\sqrt{x}+5\sin(x))
limit as x approaches 5-of 3/(x^2-25)	\lim\:_{x\to\:5-}(\frac{3}{x^{2}-25})
derivative of f(x)=19e^{x^2}	derivative\:f(x)=19e^{x^{2}}
f(x)=e^{e^x}	f(x)=e^{e^{x}}
y*e^{2x}dx=(1+e^{2x})dy	y\cdot\:e^{2x}dx=(1+e^{2x})dy
laplacetransform cos(25pit+pi/2)	laplacetransform\:\cos(25πt+\frac{π}{2})
(dy)/(dx)=xy-y	\frac{dy}{dx}=xy-y
d/(dy)((x+y)/(xy))	\frac{d}{dy}(\frac{x+y}{xy})
derivative of y=sin^4(x)	derivative\:y=\sin^{4}(x)
integral from 0 to 2 of pi(2x)^2	\int\:_{0}^{2}π(2x)^{2}dx
limit as x approaches-3 of 8+x	\lim\:_{x\to\:-3}(8+x)
derivative of e^{6xcos(x})	\frac{d}{dx}(e^{6x\cos(x)})
(\partial)/(\partial y)(xy^2+bx^2y)	\frac{\partial\:}{\partial\:y}(xy^{2}+bx^{2}y)
derivative of-xy	\frac{d}{dx}(-xy)
derivative of y=e^{4cos(sqrt(x))}	derivative\:y=e^{4\cos(\sqrt{x})}
integral of e^x+1/x	\int\:e^{x}+\frac{1}{x}dx
f(x)=sin(cos(x))	f(x)=\sin(\cos(x))
integral of 3/(x^2+2)	\int\:\frac{3}{x^{2}+2}dx
integral of 18sec^4(x)	\int\:18\sec^{4}(x)dx
limit as h approaches 0 of sin(1/h)	\lim\:_{h\to\:0}(\sin(\frac{1}{h}))
integral of 2sin^3(2x)cos^3(2x)	\int\:2\sin^{3}(2x)\cos^{3}(2x)dx
limit as x approaches+10 of x	\lim\:_{x\to\:+10}(x)
(dy)/(dx)=x^6y^{-7},y(0)=4	\frac{dy}{dx}=x^{6}y^{-7},y(0)=4
x(dy)/(dx)-(1-x)y=xy^2	x\frac{dy}{dx}-(1-x)y=xy^{2}
derivative of f(x)=e^{-x}-e^{-x}x	derivative\:f(x)=e^{-x}-e^{-x}x
derivative of arcsin(cos(x))	\frac{d}{dx}(\arcsin(\cos(x)))
inverse oflaplace (s+1)/(s(s-1)^2)	inverselaplace\:\frac{s+1}{s(s-1)^{2}}
(\partial)/(\partial x)(e^{-(x+y)})	\frac{\partial\:}{\partial\:x}(e^{-(x+y)})
(t^2-1)y^'+2ty^2=0	(t^{2}-1)y^{\prime\:}+2ty^{2}=0
integral of (t^2)/((a+bt^3)^2)	\int\:\frac{t^{2}}{(a+bt^{3})^{2}}dt
xy^'=2x^2y+3x^3e^{x^2}	xy^{\prime\:}=2x^{2}y+3x^{3}e^{x^{2}}
integral from 4 to 9 of 1/(5-sqrt(x))	\int\:_{4}^{9}\frac{1}{5-\sqrt{x}}dx
integral of x^2sqrt(x-5)	\int\:x^{2}\sqrt{x-5}dx
limit as x approaches infinity of xln(1)	\lim\:_{x\to\:\infty\:}(x\ln(1))
derivative of (2x-5)/(sqrt(x))	derivative\:\frac{2x-5}{\sqrt{x}}
(dy)/(dx)=2xsqrt(x-7)	\frac{dy}{dx}=2x\sqrt{x-7}
limit as x approaches-2 of (3x)/(x+2)	\lim\:_{x\to\:-2}(\frac{3x}{x+2})
integral of 5x^{3/7}	\int\:5x^{\frac{3}{7}}dx
derivative of x^2-12	derivative\:x^{2}-12
derivative of f(x)=((2x)/3 x+3/2 x)2	derivative\:f(x)=(\frac{2x}{3}x+\frac{3}{2}x)2
derivative of arccosh(sec(x))	\frac{d}{dx}(\arccosh(\sec(x)))
slope of (13,0),(-2,-12)	slope\:(13,0),(-2,-12)
derivative of y=(x-5)(x+3)(x+4)	derivative\:y=(x-5)(x+3)(x+4)
integral from 1 to 6 of xln(x)	\int\:_{1}^{6}x\ln(x)dx
(\partial)/(\partial x)(sin(6x))	\frac{\partial\:}{\partial\:x}(\sin(6x))
slope ofintercept (46,381),(64,444)	slopeintercept\:(46,381),(64,444)
(\partial)/(\partial x)(4y^2)	\frac{\partial\:}{\partial\:x}(4y^{2})
tangent of y=5x^3-5x	tangent\:y=5x^{3}-5x
y^{''}-a^2y=0	y^{\prime\:\prime\:}-a^{2}y=0
integral from 0 to 2 of e^{2t}	\int\:_{0}^{2}e^{2t}dt
area 3-x^2,-1	area\:3-x^{2},-1
y^{''}+4y^'+25y=0	y^{\prime\:\prime\:}+4y^{\prime\:}+25y=0
sum from n=1 to infinity of (5n)/(n^2+4)	\sum\:_{n=1}^{\infty\:}\frac{5n}{n^{2}+4}
tangent of y=x^2-3x-5,(2,-7)	tangent\:y=x^{2}-3x-5,(2,-7)
derivative of (6000/x)	\frac{d}{dx}(\frac{6000}{x})
integral of sin^6(x)cos^3(x)	\int\:\sin^{6}(x)\cos^{3}(x)dx
limit as x approaches 0 of x^{7x}	\lim\:_{x\to\:0}(x^{7x})
inverse oflaplace 3/(s^2+16)	inverselaplace\:\frac{3}{s^{2}+16}
sum from n=2 to infinity of (1/2)^n	\sum\:_{n=2}^{\infty\:}(\frac{1}{2})^{n}
integral of 1/(2sin(x)cos(x))	\int\:\frac{1}{2\sin(x)\cos(x)}dx
derivative of 2xln(x+x)	\frac{d}{dx}(2x\ln(x)+x)
derivative of 1500x+3000(3x+3)^{-1}-1000	derivative\:1500x+3000(3x+3)^{-1}-1000
area x^{2/7},1,x=0	area\:x^{\frac{2}{7}},1,x=0
derivative of 8xy	derivative\:8xy
(2x+2/y)+((2x^2)/y+(2x)/(y^2))y^'=0	(2x+\frac{2}{y})+(\frac{2x^{2}}{y}+\frac{2x}{y^{2}})y^{\prime\:}=0
derivative of x(sqrt(x)+1)	\frac{d}{dx}(x(\sqrt{x}+1))
integral from 0 to 4 of f(x)	\int\:_{0}^{4}f(x)dx
(x-2)y^'+y=3x^2+2x	(x-2)y^{\prime\:}+y=3x^{2}+2x
sum from n=0 to infinity of 1/((2n+1)^4)	\sum\:_{n=0}^{\infty\:}\frac{1}{(2n+1)^{4}}
area x+3y=34,x+6=y^2	area\:x+3y=34,x+6=y^{2}
derivative of 9x^2e^{-x}	\frac{d}{dx}(9x^{2}e^{-x})
derivative of f(x)=sqrt(5/2+3/2 x)	derivative\:f(x)=\sqrt{\frac{5}{2}+\frac{3}{2}x}
integral of x^2\sqrt[3]{(x)(x^4)(x^3)}	\int\:x^{2}\sqrt[3]{(x)(x^{4})(x^{3})}dx
derivative of (arctan(7x))^2	derivative\:(\arctan(7x))^{2}
sum from n=0 to infinity of 4/(3^{n-1)}	\sum\:_{n=0}^{\infty\:}\frac{4}{3^{n-1}}
limit as x approaches 0 of 2/(e^x)	\lim\:_{x\to\:0}(\frac{2}{e^{x}})
(dy)/(dx)+5y=xe^{-5x}	\frac{dy}{dx}+5y=xe^{-5x}
tangent of (8x)/(x^2+1)	tangent\:\frac{8x}{x^{2}+1}
integral of \sqrt[3]{((2t)/3)^2}	\int\:\sqrt[3]{(\frac{2t}{3})^{2}}dt
slope of (20,8),(9,16)	slope\:(20,8),(9,16)
integral from 0 to 5 of (x-1)/(x^2-5x-6)	\int\:_{0}^{5}\frac{x-1}{x^{2}-5x-6}dx
derivative of (3x+36/(2sqrt(x+18)))	\frac{d}{dx}(\frac{3x+36}{2\sqrt{x+18}})
(x+y)y^'=y	(x+y)y^{\prime\:}=y
integral of (e^x)/((e^x-7)(e^{2x)+1)}	\int\:\frac{e^{x}}{(e^{x}-7)(e^{2x}+1)}dx
f(x)=xcos(2x)	f(x)=x\cos(2x)
integral of xsqrt(x+11)	\int\:x\sqrt{x+11}dx
derivative of 4/(2+2x^2)	derivative\:\frac{4}{2+2x^{2}}
integral of e^{-(x^2)}	\int\:e^{-(x^{2})}dx
taylor x^3,1	taylor\:x^{3},1
(1+t^2)(dy)/(dt)+4ty=(1+t^2)^{-2}	(1+t^{2})\frac{dy}{dt}+4ty=(1+t^{2})^{-2}
limit as x approaches infinity+of e^x	\lim\:_{x\to\:\infty\:+}(e^{x})
integral from 0 to 3 of 0.2e^{-0.2x}	\int\:_{0}^{3}0.2e^{-0.2x}dx
integral of 20sin^2(xco)s^2x	\int\:20\sin^{2}(xco)s^{2}xdx

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