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Popular Calculus Problems

derivative of g(x)= 1/(4x^2+2x)	derivative\:g(x)=\frac{1}{4x^{2}+2x}
laplacetransform 2t+3t*cos(2t)	laplacetransform\:2t+3t\cdot\:\cos(2t)
derivative of cxe^{-x}	\frac{d}{dx}(cxe^{-x})
integral of 2x*sin(x)e^x	\int\:2x\cdot\:\sin(x)e^{x}dx
t*ty^{''}+5ty^'+4y=0	t\cdot\:ty^{\prime\:\prime\:}+5ty^{\prime\:}+4y=0
((sqrt(x^2+25))/2+(9-x)/3)^'	(\frac{\sqrt{x^{2}+25}}{2}+\frac{9-x}{3})^{\prime\:}
integral of x^7-4x^{-3}+1	\int\:x^{7}-4x^{-3}+1dx
integral of 4xe^{-x^2}	\int\:4xe^{-x^{2}}dx
y^'+y=-1	y^{\prime\:}+y=-1
derivative of tan(arccos(x))	\frac{d}{dx}(\tan(\arccos(x)))
integral from 0 to 1 of (x+1)^3	\int\:_{0}^{1}(x+1)^{3}dx
limit as x approaches-1 of 2-3x	\lim\:_{x\to\:-1}(2-3x)
limit as x approaches infinity of 8-2x	\lim\:_{x\to\:\infty\:}(8-2x)
(\partial)/(\partial y)(x^2+y^2-1)	\frac{\partial\:}{\partial\:y}(x^{2}+y^{2}-1)
derivative of-(14/(x^6))	\frac{d}{dx}(-\frac{14}{x^{6}})
expand 4(2t-5)^2	expand\:4(2t-5)^{2}
integral of x^2*sqrt(x^2-9)	\int\:x^{2}\cdot\:\sqrt{x^{2}-9}dx
(dP)/(dt)=0.5(P)(1-P/(1000))	\frac{dP}{dt}=0.5(P)(1-\frac{P}{1000})
(dy)/(dx)=(3sec(y))/((x+1)^2)	\frac{dy}{dx}=\frac{3\sec(y)}{(x+1)^{2}}
derivative of f(x)=(4x)/((x^2+1)^2)	derivative\:f(x)=\frac{4x}{(x^{2}+1)^{2}}
sum from n=1 to infinity of n(sin(npi))	\sum\:_{n=1}^{\infty\:}n(\sin(nπ))
derivative of (1-x^2(1+x)^3)	\frac{d}{dx}((1-x)^{2}(1+x)^{3})
sum from n=1 to infinity of (3n)/(-2n+5)	\sum\:_{n=1}^{\infty\:}\frac{3n}{-2n+5}
derivative of 2e^{3t}	derivative\:2e^{3t}
derivative of 3600(1-t/(60))^2	derivative\:3600(1-\frac{t}{60})^{2}
limit as x approaches 3 of (\|x+3\|)/(x+3)	\lim\:_{x\to\:3}(\frac{\left\|x+3\right\|}{x+3})
derivative of 4/(x^4+1/x+2)	\frac{d}{dx}(\frac{4}{x^{4}}+\frac{1}{x}+2)
limit as x approaches 0 of (1+sin(3x))^{1/x}	\lim\:_{x\to\:0}((1+\sin(3x))^{\frac{1}{x}})
derivative of (pix^2/2)	\frac{d}{dx}(\frac{πx^{2}}{2})
derivative of (1+sin(x)cos(x))	\frac{d}{dx}((1+\sin(x))\cos(x))
(\partial)/(\partial y)(3x^2-3)	\frac{\partial\:}{\partial\:y}(3x^{2}-3)
integral of (7x^6+6)/(x^7+6x)	\int\:\frac{7x^{6}+6}{x^{7}+6x}dx
integral of sqrt(e^{10x)-9}	\int\:\sqrt{e^{10x}-9}dx
sum from n=3 to infinity of 2/(5^n)	\sum\:_{n=3}^{\infty\:}\frac{2}{5^{n}}
limit as x approaches 0+of x+\|x\|	\lim\:_{x\to\:0+}(x+\left\|x\right\|)
derivative of (3x^2+4^2(4x^2-8)^2)	\frac{d}{dx}((3x^{2}+4)^{2}(4x^{2}-8)^{2})
y^{''}+8y^'+16y=0,y(1)=0,y^'(1)=1	y^{\prime\:\prime\:}+8y^{\prime\:}+16y=0,y(1)=0,y^{\prime\:}(1)=1
derivative of (x^4+3x^2-2)^5	derivative\:(x^{4}+3x^{2}-2)^{5}
(x+1)y^'+(x+2)y=8xe^{-x}	(x+1)y^{\prime\:}+(x+2)y=8xe^{-x}
integral of 8x^3e^{x^4}	\int\:8x^{3}e^{x^{4}}dx
derivative of 8sqrt(x)sin(x)	derivative\:8\sqrt{x}\sin(x)
area 1-x^2,13-7x	area\:1-x^{2},13-7x
(\partial)/(\partial x)(e^{8x}cos(5y))	\frac{\partial\:}{\partial\:x}(e^{8x}\cos(5y))
derivative of 5csc(x)	\frac{d}{dx}(5\csc(x))
limit as x approaches a of x^2	\lim\:_{x\to\:a}(x^{2})
integral of 1/(t^2)sin(8/t+3)	\int\:\frac{1}{t^{2}}\sin(\frac{8}{t}+3)dt
inverse oflaplace 3+1/s	inverselaplace\:3+\frac{1}{s}
integral from o to 1 of 42x(1-x)^5	\int\:_{o}^{1}42x(1-x)^{5}dx
derivative of a^2+x^2	\frac{d}{dx}(a^{2}+x^{2})
limit as x approaches 1 of (1+x)/(1-x^2)	\lim\:_{x\to\:1}(\frac{1+x}{1-x^{2}})
integral from 0 to-pi/6 of xcos(3x)	\int\:_{0}^{-\frac{π}{6}}x\cos(3x)dx
derivative of y=8x+7	derivative\:y=8x+7
limit as t approaches 1 of sqrt(t+8)	\lim\:_{t\to\:1}(\sqrt{t+8})
(\partial)/(\partial x)(4e^x-2x*e^y)	\frac{\partial\:}{\partial\:x}(4\cdot\:e^{x}-2\cdot\:x\cdot\:e^{y})
derivative of (4x-1^{1/3})	\frac{d}{dx}((4x-1)^{\frac{1}{3}})
derivative of (x^4+6x-1)/(7x^2-6x+1)	derivative\:\frac{x^{4}+6x-1}{7x^{2}-6x+1}
derivative of sin(15x)	derivative\:\sin(15x)
integral of sqrt(6-x^2)	\int\:\sqrt{6-x^{2}}dx
y^'=(sqrt(1-y^2))/t	y^{\prime\:}=\frac{\sqrt{1-y^{2}}}{t}
tangent of f(x)=4x^2+2x,(-2,12)	tangent\:f(x)=4x^{2}+2x,(-2,12)
integral of (x^7)/2-1/(x^5)	\int\:\frac{x^{7}}{2}-\frac{1}{x^{5}}dx
limit as n approaches infinity of sin(2n)	\lim\:_{n\to\:\infty\:}(\sin(2n))
taylor e^{-3x},0	taylor\:e^{-3x},0
sum from n=2 to infinity of x^n	\sum\:_{n=2}^{\infty\:}x^{n}
(dy}{dx}=-\frac{sin(x))/y	\frac{dy}{dx}=-\frac{\sin(x)}{y}
integral of cos(r^2)	\int\:\cos(r^{2})dr
xy^'=(1-x)y+x^2+x^3	xy^{\prime\:}=(1-x)y+x^{2}+x^{3}
y^{''}+4y^'=cos^2(x)	y^{\prime\:\prime\:}+4y^{\prime\:}=\cos^{2}(x)
integral of-1/(10-x)	\int\:-\frac{1}{10-x}dx
integral of cos^3(x)(sin(x))	\int\:\cos^{3}(x)(\sin(x))dx
area y=x^2-8,y=1	area\:y=x^{2}-8,y=1
derivative of y=5e^{5t+1}	derivative\:y=5e^{5t+1}
derivative of ln(cos(x)+x)	\frac{d}{dx}(\ln(\cos(x))+x)
integral of (x^2)/((9x^2-4)^{5/2)}	\int\:\frac{x^{2}}{(9x^{2}-4)^{\frac{5}{2}}}dx
integral from 0 to pi of (5e^x+3sin(x))	\int\:_{0}^{π}(5e^{x}+3\sin(x))dx
(\partial)/(\partial x)(3tsin^2(t))	\frac{\partial\:}{\partial\:x}(3t\sin^{2}(t))
derivative of f(x)=5x-1	derivative\:f(x)=5x-1
x^4y^'+3x^3y=x^2e^x	x^{4}y^{\prime\:}+3x^{3}y=x^{2}e^{x}
derivative of (3x-9/(2x+4))	\frac{d}{dx}(\frac{3x-9}{2x+4})
integral of 1/(sqrt(16x^2+25))	\int\:\frac{1}{\sqrt{16x^{2}+25}}dx
integral of sqrt(15-2x-x^2)	\int\:\sqrt{15-2x-x^{2}}dx
(dy)/(dt)+k(340-y)=0	\frac{dy}{dt}+k(340-y)=0
laplacetransform e	laplacetransform\:e
integral of-4x^2(4x^3-1)^7	\int\:-4x^{2}(4x^{3}-1)^{7}dx
f(x)=x^{2x}	f(x)=x^{2x}
derivative of a(e^x+e^{xx})	\frac{d}{dx}(a(e^{x}+e^{xx}))
derivative of f(x)= 1/(sqrt(x+1))	derivative\:f(x)=\frac{1}{\sqrt{x+1}}
limit as x approaches infinity of y^{-x}	\lim\:_{x\to\:\infty\:}(y^{-x})
limit as x approaches 2 of 5	\lim\:_{x\to\:2}(5)
area e^{-x},0,0,ln(3)	area\:e^{-x},0,0,\ln(3)
(dy)/(dt)=6y+2t-4,y(0)=3	\frac{dy}{dt}=6y+2t-4,y(0)=3
limit as x approaches 4 of (x^2)/(x-4)	\lim\:_{x\to\:4}(\frac{x^{2}}{x-4})
integral of 12xln(2x)	\int\:12x\ln(2x)dx
derivative of e^{x*y}	\frac{d}{dx}(e^{x\cdot\:y})
parity f(x)=sin(tan(sqrt(1+x^3)))	parity\:f(x)=\sin(\tan(\sqrt{1+x^{3}}))
limit as x approaches 3 of x/2	\lim\:_{x\to\:3}(\frac{x}{2})
derivative of 1/(arcsec(x))	\frac{d}{dx}(\frac{1}{\arcsec(x)})
d/(dt)(cos(wt))	\frac{d}{dt}(\cos(wt))
integral of 2e^xcos(x)	\int\:2e^{x}\cos(x)dx
(\partial)/(\partial y)(e^y)	\frac{\partial\:}{\partial\:y}(e^{y})

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