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Popular Calculus Problems

limit as x approaches infinity of-3/x	\lim\:_{x\to\:\infty\:}(-\frac{3}{x})
y^'+3(tan(3x))y=-2cos(3x)	y^{\prime\:}+3(\tan(3x))y=-2\cos(3x)
integral from 0 to 7 of (5t)/((t-8)^2)	\int\:_{0}^{7}\frac{5t}{(t-8)^{2}}dt
(\partial)/(\partial x)(e^{(-0.1xy)})	\frac{\partial\:}{\partial\:x}(e^{(-0.1xy)})
(\partial)/(\partial x)(e^xcos(y)+yz)	\frac{\partial\:}{\partial\:x}(e^{x}\cos(y)+yz)
derivative of (x(x+10)/((x+5)^2))	\frac{d}{dx}(\frac{x(x+10)}{(x+5)^{2}})
limit as x approaches 1 of (2x-3)*(x+1)	\lim\:_{x\to\:1}((2x-3)\cdot\:(x+1))
y^{''}+1.5y^'-y=12x^2+6x^3-x^4	y^{\prime\:\prime\:}+1.5y^{\prime\:}-y=12x^{2}+6x^{3}-x^{4}
derivative of e^{mt}*sin(nt)	\frac{d}{dx}(e^{mt}\cdot\:\sin(nt))
derivative of f(x)=3cos(2ln(x))	derivative\:f(x)=3\cos(2\ln(x))
x(dy)/(dx)+y=sqrt(x)	x\frac{dy}{dx}+y=\sqrt{x}
y^'+6y=e^{4t},y(0)=2	y^{\prime\:}+6y=e^{4t},y(0)=2
integral of (x^2)/(sqrt(20-4x+x^2))	\int\:\frac{x^{2}}{\sqrt{20-4x+x^{2}}}dx
derivative of 0.5sin^2(x-x+1)	\frac{d}{dx}(0.5\sin^{2}(x)-x+1)
inverse oflaplace 4/((s+1)^2)	inverselaplace\:\frac{4}{(s+1)^{2}}
t*y^'+ty=1-y	t\cdot\:y^{\prime\:}+ty=1-y
laplacetransform t^2e^{at}	laplacetransform\:t^{2}\cdot\:e^{a\cdot\:t}
t^2y^{''}+19ty^'+81y=0	t^{2}y^{\prime\:\prime\:}+19ty^{\prime\:}+81y=0
integral of sqrt(1+cot^2(x))	\int\:\sqrt{1+\cot^{2}(x)}dx
integral from 0 to 5 of \|15-5t\|	\int\:_{0}^{5}\left\|15-5t\right\|dt
derivative of f(xx^'(x))	\frac{d}{dx}(f(x)x^{\prime\:}(x))
(\partial)/(\partial x)(ln(8x^2+3y^2+3))	\frac{\partial\:}{\partial\:x}(\ln(8x^{2}+3y^{2}+3))
integral of (10x^4-9x^2)/(2x^5-3x^3+14)	\int\:\frac{10x^{4}-9x^{2}}{2x^{5}-3x^{3}+14}dx
y^{'''}+3y^{''}+3y^'+y=0	y^{\prime\:\prime\:\prime\:}+3y^{\prime\:\prime\:}+3y^{\prime\:}+y=0
(\partial)/(\partial x)((5y)/(x^3))	\frac{\partial\:}{\partial\:x}(\frac{5y}{x^{3}})
y^{''}-9y^'+18y=5sin(4t),y(0)=5,y^'(0)=2	y^{\prime\:\prime\:}-9y^{\prime\:}+18y=5\sin(4t),y(0)=5,y^{\prime\:}(0)=2
taylor xe^{-3x}	taylor\:xe^{-3x}
integral of e^xsqrt(81-e^{2x)}	\int\:e^{x}\sqrt{81-e^{2x}}dx
y^'-y=3te^{2t}	y^{\prime\:}-y=3te^{2t}
(\partial)/(\partial x)(sqrt(3x+2y))	\frac{\partial\:}{\partial\:x}(\sqrt{3x+2y})
integral of 1/(sqrt(9x^2+6x-8))	\int\:\frac{1}{\sqrt{9x^{2}+6x-8}}dx
sum from n=0 to infinity of n 1/(5^n)	\sum\:_{n=0}^{\infty\:}n\frac{1}{5^{n}}
integral of sec^2(3xta)n^53x	\int\:\sec^{2}(3xta)n^{5}3xdx
yln(x)(dy}{dx}=(\frac{(y+1))/x)^2	y\ln(x)\frac{dy}{dx}=(\frac{(y+1)}{x})^{2}
derivative of (x^2-7)^2	derivative\:(x^{2}-7)^{2}
(\partial)/(\partial x)(ln(cos^2(x)+1))	\frac{\partial\:}{\partial\:x}(\ln(\cos^{2}(x)+1))
tangent of f(x)= x/((5x-4)^8),\at x=1	tangent\:f(x)=\frac{x}{(5x-4)^{8}},\at\:x=1
slope of (-2.2)(5.3)	slope\:(-2.2)(5.3)
tangent of y=x(x+1)^5,(1,32)	tangent\:y=x(x+1)^{5},(1,32)
integral from 3/4 to 1 of 2x	\int\:_{\frac{3}{4}}^{1}2xdx
(dy)/(dx)+y^9x+6y=0	\frac{dy}{dx}+y^{9}x+6y=0
y^{''}+2y^'+y=e-tln(t)	y^{\prime\:\prime\:}+2y^{\prime\:}+y=e-t\ln(t)
(\partial)/(\partial y)(((x-y))/(x+y))	\frac{\partial\:}{\partial\:y}(\frac{(x-y)}{x+y})
integral from-1 to 2 of (x^2-1)	\int\:_{-1}^{2}(x^{2}-1)dx
limit as x approaches 2 of 3/((x-2)^3)	\lim\:_{x\to\:2}(\frac{3}{(x-2)^{3}})
integral of (e^{2x})/((e^{2x)+1)^3}	\int\:\frac{e^{2x}}{(e^{2x}+1)^{3}}dx
derivative of log_{5}(sin^2(x))	\frac{d}{dx}(\log_{5}(\sin^{2}(x)))
integral of sqrt(441-x^2)	\int\:\sqrt{441-x^{2}}dx
limit as x approaches 0-of (x+1)/(x^2)	\lim\:_{x\to\:0-}(\frac{x+1}{x^{2}})
integral of 17sin^3(xco)s^2x	\int\:17\sin^{3}(xco)s^{2}xdx
(dy)/(dx)=10^{-21}*y^3	\frac{dy}{dx}=10^{-21}\cdot\:y^{3}
derivative of y=e^{arctan(3t^2)}	derivative\:y=e^{\arctan(3t^{2})}
derivative of 5xsin(pix)	\frac{d}{dx}(5x\sin(πx))
derivative of (3000/(x+3600x^{-1)})	\frac{d}{dx}(\frac{3000}{x+3600x^{-1}})
inverse oflaplace 9/(s(s^2+2s+9))	inverselaplace\:\frac{9}{s(s^{2}+2s+9)}
tangent of f(x)= 1/(x+1),(-2,-1)	tangent\:f(x)=\frac{1}{x+1},(-2,-1)
derivative of (6x^2+7x^4)	\frac{d}{dx}((6x^{2}+7x)^{4})
maclaurin e^{x^2+x}	maclaurin\:e^{x^{2}+x}
derivative of 3x^2y+y^3-3x^2-3y^2+2	\frac{d}{dx}(3x^{2}y+y^{3}-3x^{2}-3y^{2}+2)
integral of 3/(2x+7)	\int\:\frac{3}{2x+7}dx
integral from 1 to e of (1/x)	\int\:_{1}^{e}(\frac{1}{x})dx
derivative of 4e^{-4x}	\frac{d}{dx}(4e^{-4x})
integral of 3(2t+5)^3	\int\:3(2t+5)^{3}dt
derivative of arctan(ln(2x+1))	\frac{d}{dx}(\arctan(\ln(2x+1)))
integral of ((82x+8))/((9x+1)(x-1))	\int\:\frac{(82x+8)}{(9x+1)(x-1)}dx
y^'+2y=4t,y(0)=3	y^{\prime\:}+2y=4t,y(0)=3
derivative of x^{-1}	derivative\:x^{-1}
derivative of (9(5^x)/(x^5))	\frac{d}{dx}(\frac{9(5^{x})}{x^{5}})
y^{''}+2y^'+17y=0	y^{\prime\:\prime\:}+2y^{\prime\:}+17y=0
derivative of 1/(sqrt(x^2+9))	\frac{d}{dx}(\frac{1}{\sqrt{x^{2}+9}})
integral of (5x^2)/(x^2+7)	\int\:\frac{5x^{2}}{x^{2}+7}dx
integral of sin^3(ax)	\int\:\sin^{3}(ax)dx
area sin(x),sin(2x),[0, pi/3 ]	area\:\sin(x),\sin(2x),[0,\frac{π}{3}]
derivative of f(x)= 1/x-2x	derivative\:f(x)=\frac{1}{x}-2x
derivative of 3/4 x^2-5x^3	\frac{d}{dx}(\frac{3}{4}x^{2}-5x^{3})
integral of 1/(-2x)	\int\:\frac{1}{-2x}dx
laplacetransform cos^2(25t)	laplacetransform\:\cos^{2}(25t)
derivative of sqrt(5)x-sqrt(2x)	derivative\:\sqrt{5}x-\sqrt{2x}
derivative of cos(2/x)	derivative\:\cos(\frac{2}{x})
integral of sin(4x-2)	\int\:\sin(4x-2)dx
derivative of h(x)=xcos(x)+3pi	derivative\:h(x)=x\cos(x)+3π
limit as x approaches 4 of cos((pix)/3)	\lim\:_{x\to\:4}(\cos(\frac{πx}{3}))
integral of (4e^x)/(e^{2x)+6e^x+9}	\int\:\frac{4e^{x}}{e^{2x}+6e^{x}+9}dx
derivative of y=3.6sqrt(x)+500	derivative\:y=3.6\sqrt{x}+500
derivative of 2x^3-15x^2-36x	\frac{d}{dx}(2x^{3}-15x^{2}-36x)
derivative of-4e^{-5x^2}	derivative\:-4e^{-5x^{2}}
limit as x approaches 0 of tan(6x)	\lim\:_{x\to\:0}(\tan(6x))
(dy)/(dx)=2sec^2(x)	\frac{dy}{dx}=2\sec^{2}(x)
sum from n=0 to infinity of e^{-na}	\sum\:_{n=0}^{\infty\:}e^{-na}
derivative of 6^{sin(pix)}	derivative\:6^{\sin(πx)}
integral from 0 to infinity of te^{-t}	\int\:_{0}^{\infty\:}te^{-t}dt
tangent of x/(x^2+49)	tangent\:\frac{x}{x^{2}+49}
limit as t approaches 2 of (t^2-4)/(t-2)	\lim\:_{t\to\:2}(\frac{t^{2}-4}{t-2})
x^'+4x=te^{-4t}	x^{\prime\:}+4x=te^{-4t}
derivative of e^ysin(xy)	\frac{d}{dx}(e^{y}\sin(xy))
limit as x approaches-infinity of 2x-x^2	\lim\:_{x\to\:-\infty\:}(2x-x^{2})
integral of 2xsqrt(x^2-1)	\int\:2x\sqrt{x^{2}-1}dx
sum from n=0 to infinity of (-0.6)^n	\sum\:_{n=0}^{\infty\:}(-0.6)^{n}
derivative of (0.3(5^x))/(x^3)	derivative\:\frac{0.3(5^{x})}{x^{3}}
taylor cos(x^2),0	taylor\:\cos(x^{2}),0

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