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Popular Calculus Problems

derivative of 1/(1-2/x)	\frac{d}{dx}(\frac{1}{1-\frac{2}{x}})
d/(dt)(cos(8t))	\frac{d}{dt}(\cos(8t))
y^'= 1/((t*y+y+t+1)),y(0)=-1	y^{\prime\:}=\frac{1}{(t\cdot\:y+y+t+1)},y(0)=-1
tangent of f(x)=sqrt(x+35),(1,6)	tangent\:f(x)=\sqrt{x+35},(1,6)
(dy)/(dx)+x^{-1}y=xy^2	\frac{dy}{dx}+x^{-1}y=xy^{2}
laplacetransform e^{-t}cos(4t)	laplacetransform\:e^{-t}\cos(4t)
integral of (3x^2+2x)e^{(x^3+x^2)}	\int\:(3x^{2}+2x)e^{(x^{3}+x^{2})}dx
tangent of f(x)=-x^3-4x-3,\at x=-1	tangent\:f(x)=-x^{3}-4x-3,\at\:x=-1
inverse oflaplace 1/((s-2)(s-2))	inverselaplace\:\frac{1}{(s-2)(s-2)}
derivative of (x^2+x)e^x	derivative\:(x^{2}+x)e^{x}
limit as x approaches 1+of 1/(1-x)	\lim\:_{x\to\:1+}(\frac{1}{1-x})
8x^2y^'=y^'+6xe^{-y}	8x^{2}y^{\prime\:}=y^{\prime\:}+6xe^{-y}
integral of (e^{2y}-y)/(e^y)	\int\:\frac{e^{2y}-y}{e^{y}}dy
integral of 9.8*e^{-0.4x}	\int\:9.8\cdot\:e^{-0.4x}dx
integral of ((sqrt(x)+8)^3)/(2sqrt(x))	\int\:\frac{(\sqrt{x}+8)^{3}}{2\sqrt{x}}dx
derivative of f(x)=10x^2	derivative\:f(x)=10x^{2}
limit as x approaches 1 of 0	\lim\:_{x\to\:1}(0)
derivative of f(x)=3x^2+5x	derivative\:f(x)=3x^{2}+5x
limit as x approaches 1 of (x+6)/(x-1)	\lim\:_{x\to\:1}(\frac{x+6}{x-1})
limit as x approaches 5+of (\|x-5\|)/(5-x)	\lim\:_{x\to\:5+}(\frac{\left\|x-5\right\|}{5-x})
integral of 8/(x^2-4)	\int\:\frac{8}{x^{2}-4}dx
y^{''}=3y	y^{\prime\:\prime\:}=3y
area y=0,y=x^2-x	area\:y=0,y=x^{2}-x
integral of (sec(x)+cos(x))/(2cos(x))	\int\:\frac{\sec(x)+\cos(x)}{2\cos(x)}dx
integral of 5/(x-4)	\int\:\frac{5}{x-4}dx
3x(dy)/(dx)+y=0,y(1)=1	3x\frac{dy}{dx}+y=0,y(1)=1
limit as (x,y) approaches (infinity,infinity) of xy	\lim\:_{(x,y)\to\:(infinity,infinity)}(xy)
tangent of y=8x+9cos(x),(0,9)	tangent\:y=8x+9\cos(x),(0,9)
integral of (e^x)/(x^2)	\int\:\frac{e^{x}}{x^{2}}dx
derivative of (e^{2x-1}/((x^2+5x)))	\frac{d}{dx}(\frac{e^{2x-1}}{(x^{2}+5x)})
tangent of 1+sqrt(4-x)	tangent\:1+\sqrt{4-x}
derivative of 1/(4y)	derivative\:\frac{1}{4y}
2ydx+xdy=0	2ydx+xdy=0
integral of ((x^2+1))/(x+1)	\int\:\frac{(x^{2}+1)}{x+1}dx
integral from 0 to 5 of 1/(sqrt(25+x^2))	\int\:_{0}^{5}\frac{1}{\sqrt{25+x^{2}}}dx
integral of c/(x^2)	\int\:\frac{c}{x^{2}}dx
derivative of f(x)=7x^{15}	derivative\:f(x)=7x^{15}
integral from 0 to 5 of 1/(x^{18/19)}	\int\:_{0}^{5}\frac{1}{x^{\frac{18}{19}}}dx
tangent of f(x)= 3/(4x+1),\at x=-1	tangent\:f(x)=\frac{3}{4x+1},\at\:x=-1
derivative of (e^{arctan(x})/(1+x^2))	\frac{d}{dx}(\frac{e^{\arctan(x)}}{1+x^{2}})
derivative of (csc(3x)/(x^3))	\frac{d}{dx}(\frac{\csc(3x)}{x^{3}})
integral of (x-4)/(x^9)	\int\:\frac{x-4}{x^{9}}dx
derivative of x^{5/3}	\frac{d}{dx}(x^{\frac{5}{3}})
laplacetransform 2te^{-5t}	laplacetransform\:2te^{-5t}
derivative of 10x-1.86x^2	\frac{d}{dx}(10x-1.86x^{2})
(\partial)/(\partial x)(y^{8x})	\frac{\partial\:}{\partial\:x}(y^{8x})
limit as x approaches 1/2 of (x^2)/(x-1)	\lim\:_{x\to\:\frac{1}{2}}(\frac{x^{2}}{x-1})
derivative of y=tan^2(9x)	derivative\:y=\tan^{2}(9x)
x(dy)/(dx)+y=x	x\frac{dy}{dx}+y=x
integral of (xe^{3x})	\int\:(xe^{3x})dx
integral of 1/(xln(4x))	\int\:\frac{1}{x\ln(4x)}dx
derivative of y=((4x^2-5)/(2-x))^3	derivative\:y=(\frac{4x^{2}-5}{2-x})^{3}
y^'-2/x y=(y^3)/(x^2),y(1)=1	y^{\prime\:}-\frac{2}{x}y=\frac{y^{3}}{x^{2}},y(1)=1
d/(ds)(1/(s^2-1))	\frac{d}{ds}(\frac{1}{s^{2}-1})
integral of (csc(θ))/(csc(θ)-sin(θ))	\int\:\frac{\csc(θ)}{\csc(θ)-\sin(θ)}dθ
integral of 5e^{-2t}sin(t)	\int\:5e^{-2t}\sin(t)dt
integral of (x+2)^2(2-x)^6	\int\:(x+2)^{2}(2-x)^{6}dx
tangent of x^3+3x^2-9x	tangent\:x^{3}+3x^{2}-9x
integral of \sqrt[6]{cot(x)}csc^2(x)	\int\:\sqrt[6]{\cot(x)}\csc^{2}(x)dx
integral from 0 to 1 of 1-x^2	\int\:_{0}^{1}1-x^{2}dx
laplacetransform e^{-,\at}	laplacetransform\:e^{-,\at\:}
d/(dθ)(sin(θ/2))	\frac{d}{dθ}(\sin(\frac{θ}{2}))
(dy}{dx}=\frac{4x)/y ,y(2)=-2	\frac{dy}{dx}=\frac{4x}{y},y(2)=-2
derivative of (x+e^x(3-sqrt(x)))	\frac{d}{dx}((x+e^{x})(3-\sqrt{x}))
derivative of (x^3-3x^2+9/(x^2))	\frac{d}{dx}(\frac{x^{3}-3x^{2}+9}{x^{2}})
integral of (x-2)^5	\int\:(x-2)^{5}dx
derivative of 12x^5+45x^4-200x^3+4	\frac{d}{dx}(12x^{5}+45x^{4}-200x^{3}+4)
area y=x^2-2,y=x	area\:y=x^{2}-2,y=x
derivative of (9+x)^2((100)/(x^2)+1)	derivative\:(9+x)^{2}(\frac{100}{x^{2}}+1)
derivative of \sqrt[7]{x^2}	\frac{d}{dx}(\sqrt[7]{x^{2}})
integral of e^{-ln(x)}(1-1/x)	\int\:e^{-\ln(x)}(1-\frac{1}{x})dx
derivative of 9e^x+x	derivative\:9e^{x}+x
derivative of ln((x-1/(x+1)))	\frac{d}{dx}(\ln(\frac{x-1}{x+1}))
(x^2+1)(dy)/(dx)+2xy-x=0	(x^{2}+1)\frac{dy}{dx}+2xy-x=0
limit as x approaches-2 of (x^2+8)/(x+2)	\lim\:_{x\to\:-2}(\frac{x^{2}+8}{x+2})
x^{''}+100x=0	x^{\prime\:\prime\:}+100x=0
integral of xcos^2(x^2)	\int\:x\cos^{2}(x^{2})dx
(dy)/(dt)-(4t)/(1+4t^2)y=4t	\frac{dy}{dt}-\frac{4t}{1+4t^{2}}y=4t
(\partial)/(\partial x)(1000)	\frac{\partial\:}{\partial\:x}(1000)
derivative of f(x)=4e^{4x}	derivative\:f(x)=4e^{4x}
integral of sqrt(2(1-cos(x)))	\int\:\sqrt{2(1-\cos(x))}dx
integral of 1/(4x-1)	\int\:\frac{1}{4x-1}dx
2y^{''}-8y=0,y(-2)=2,y^'(-2)=1	2y^{\prime\:\prime\:}-8y=0,y(-2)=2,y^{\prime\:}(-2)=1
y^{''}+3y=sin(t)	y^{\prime\:\prime\:}+3y=\sin(t)
f(x)=ln(x+sqrt(x^2-1))	f(x)=\ln(x+\sqrt{x^{2}-1})
integral of (6x-5)	\int\:(6x-5)dx
derivative of log_{e}(cos(x))	\frac{d}{dx}(\log_{e}(\cos(x)))
derivative of (1+2x/((3x-1)^2))	\frac{d}{dx}(\frac{1+2x}{(3x-1)^{2}})
(y+4)(dy)/(dx)=2xy+4y	(y+4)\frac{dy}{dx}=2xy+4y
integral of (cos(6x)-csc^2(x))	\int\:(\cos(6x)-\csc^{2}(x))dx
integral of (4+10x)/(sqrt(7+4x+5x^2))	\int\:\frac{4+10x}{\sqrt{7+4x+5x^{2}}}dx
derivative of (4+sec(θ))sin(θ)	derivative\:(4+\sec(θ))\sin(θ)
derivative of e^{x^4+3x}	derivative\:e^{x^{4}+3x}
integral from 1 to 5 of 6/x	\int\:_{1}^{5}\frac{6}{x}dx
integral of 6x+8	\int\:6x+8dx
derivative of ((e^x-e^{-x})/2)	\frac{d}{dx}(\frac{(e^{x}-e^{-x})}{2})
d/(d{x)}(({x})/(({x)^2+{y}^2+{z}^2)^{3/2}})	\frac{d}{d{x}}(\frac{{x}}{({x}^{2}+{y}^{2}+{z}^{2})^{\frac{3}{2}}})
integral of (2x^2)/((x^2-1)^2)	\int\:\frac{2x^{2}}{(x^{2}-1)^{2}}dx
limit as x approaches-infinity of x-(x)	\lim\:_{x\to\:-\infty\:}(x-(x))
ydx-xdy=0	ydx-xdy=0

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