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Popular Calculus Problems

(dy)/(dx)=(x-1)/(y^3)	\frac{dy}{dx}=\frac{x-1}{y^{3}}
limit as x approaches+2 of ((1))/((x+2))	\lim\:_{x\to\:+2}(\frac{(1)}{(x+2)})
derivative of (e^{2x}^2)	\frac{d}{dx}((e^{2x})^{2})
derivative of (4-x/(5x))	\frac{d}{dx}(\frac{4-x}{5x})
integral of ((ln(x))^{32})/x	\int\:\frac{(\ln(x))^{32}}{x}dx
limit as x approaches 2 of 2x^4-10	\lim\:_{x\to\:2}(2x^{4}-10)
(\partial)/(\partial y)(y^5-3xy)	\frac{\partial\:}{\partial\:y}(y^{5}-3xy)
(d^2)/(dx^2)(ln(x^2+3x+15))	\frac{d^{2}}{dx^{2}}(\ln(x^{2}+3x+15))
f(x)=8ln(x)	f(x)=8\ln(x)
integral of 3x^2sqrt(x^3-2)	\int\:3x^{2}\sqrt{x^{3}-2}dx
y^'+3xy-3=0	y^{\prime\:}+3xy-3=0
limit as x approaches 1 of 3x^2-7x+1	\lim\:_{x\to\:1}(3x^{2}-7x+1)
integral from 0 to 1 of 2e^{-2x}	\int\:_{0}^{1}2e^{-2x}dx
derivative of-sin(x)+cos(x)+x-1/(x^2)	derivative\:-\sin(x)+\cos(x)+x-\frac{1}{x^{2}}
derivative of x^3-6x^2+8x	\frac{d}{dx}(x^{3}-6x^{2}+8x)
y^{''}+4y=8x^2	y^{\prime\:\prime\:}+4y=8x^{2}
tangent of x^3+y^3=9	tangent\:x^{3}+y^{3}=9
integral of (7x^2)ex^3+1	\int\:(7x^{2})ex^{3}+1dx
f(x)=-4sin(4x)	f(x)=-4\sin(4x)
slope ofintercept (-4,-2),(5,-7)	slopeintercept\:(-4,-2),(5,-7)
tangent of y=x+6/x ,(3,5)	tangent\:y=x+\frac{6}{x},(3,5)
derivative of 92x-(x^2)/(100)	derivative\:92x-\frac{x^{2}}{100}
(\partial)/(\partial y)(x/(4+y))	\frac{\partial\:}{\partial\:y}(\frac{x}{4+y})
81y^{''}+180y^'+125y=0,y(3)=6,y^'(3)=6	81y^{\prime\:\prime\:}+180y^{\prime\:}+125y=0,y(3)=6,y^{\prime\:}(3)=6
derivative of 8cos^2(x)	\frac{d}{dx}(8\cos^{2}(x))
area 2x^3-6x^2-2x+6,-x^3+3x^2+x-3	area\:2x^{3}-6x^{2}-2x+6,-x^{3}+3x^{2}+x-3
area y=5cos(7x),y=5-5cos(7x)	area\:y=5\cos(7x),y=5-5\cos(7x)
integral from 0 to pi/(16) of cos(8x)	\int\:_{0}^{\frac{π}{16}}\cos(8x)dx
integral from 0 to 4 of pi((20-5x)/4)^2	\int\:_{0}^{4}π(\frac{20-5x}{4})^{2}dx
derivative of y=4x^2+1	derivative\:y=4x^{2}+1
integral of 2x^3e^{x^2}	\int\:2x^{3}e^{x^{2}}dx
derivative of x+y-1	\frac{d}{dx}(x+y-1)
integral of (1/(2sqrt(x)))	\int\:(\frac{1}{2\sqrt{x}})dx
area y=sqrt(3x),x=0,x=4	area\:y=\sqrt{3x},x=0,x=4
derivative of 2^y	derivative\:2^{y}
tangent of f(x)=(2x-1)^3,\at x=1	tangent\:f(x)=(2x-1)^{3},\at\:x=1
integral of x^{-2}e^{-x}	\int\:x^{-2}e^{-x}dx
y^{''}+10y^'+34y=0	y^{\prime\:\prime\:}+10y^{\prime\:}+34y=0
xdy-ydx=2x^2y^2dy,y(1)=2	xdy-ydx=2x^{2}y^{2}dy,y(1)=2
derivative of cos(2xcos(x))	\frac{d}{dx}(\cos(2x)\cos(x))
integral of (8-3x)/(sqrt(25-64x^2))	\int\:\frac{8-3x}{\sqrt{25-64x^{2}}}dx
derivative of (x-3)(x^2+6)	derivative\:(x-3)(x^{2}+6)
(\partial)/(\partial x)(8xcos(x)cos(y))	\frac{\partial\:}{\partial\:x}(8x\cos(x)\cos(y))
limit as x approaches 1 of (\|x\|)/x	\lim\:_{x\to\:1}(\frac{\left\|x\right\|}{x})
limit as x approaches 0 of h(1/x)	\lim\:_{x\to\:0}(h(\frac{1}{x}))
integral of e^θsin(3θ)	\int\:e^{θ}\sin(3θ)dθ
integral of 5x^3e^{x^4}	\int\:5x^{3}e^{x^{4}}dx
d/(dt)(5/(5-t))	\frac{d}{dt}(\frac{5}{5-t})
tangent of x^2y^2=4,(-1,2)	tangent\:x^{2}y^{2}=4,(-1,2)
integral of sqrt(4-25x^2)	\int\:\sqrt{4-25x^{2}}dx
derivative of ln(x/4+(x-4)/x)	\frac{d}{dx}(\ln(\frac{x}{4})+\frac{x-4}{x})
derivative of f(x)=(x^2-10x+25)/(x-5)	derivative\:f(x)=\frac{x^{2}-10x+25}{x-5}
slope of (9.11)(-8.9)	slope\:(9.11)(-8.9)
(\partial)/(\partial x)(4yx)	\frac{\partial\:}{\partial\:x}(4yx)
integral of (4e^{2x}+2e^x)/(1+e^{2x)}	\int\:\frac{4e^{2x}+2e^{x}}{1+e^{2x}}dx
derivative of 4x-3x^2	\frac{d}{dx}(4x-3x^{2})
integral of 5x^5e^{-x^3}	\int\:5x^{5}e^{-x^{3}}dx
integral of x(20x^2+60x)	\int\:x(20x^{2}+60x)dx
inverse oflaplace (5+5s)/(s^2+25)	inverselaplace\:\frac{5+5s}{s^{2}+25}
tangent of x^4+2e^x	tangent\:x^{4}+2e^{x}
integral of sin(24x)	\int\:\sin(24x)dx
integral from 0 to 2 of sqrt(1+x)	\int\:_{0}^{2}\sqrt{1+x}dx
derivative of x/(1-\frac{1){x^2}}	derivative\:\frac{x}{1-\frac{1}{x^{2}}}
integral of 3(3x+9)^5	\int\:3(3x+9)^{5}dx
(t^2+2t)(dx)/(dt)=2x+7,x(1)=1	(t^{2}+2t)\frac{dx}{dt}=2x+7,x(1)=1
limit as x approaches infinity of \sqrt[x]{2+5^x}	\lim\:_{x\to\:\infty\:}(\sqrt[x]{2+5^{x}})
integral from 1 to 5 of \|x^2-6x+8\|	\int\:_{1}^{5}\left\|x^{2}-6x+8\right\|dx
integral of 7x^4-5x^3+5x^2+C	\int\:7x^{4}-5x^{3}+5x^{2}+Cdx
area 7/x ,x=1,x=41	area\:\frac{7}{x},x=1,x=41
limit as x approaches-7-of x^2+7	\lim\:_{x\to\:-7-}(x^{2}+7)
(dy)/(dx)=2+2y+x+xy	\frac{dy}{dx}=2+2y+x+xy
derivative of f(x)=cx^{-2}	derivative\:f(x)=cx^{-2}
(\partial)/(\partial y)(xy+x^2)	\frac{\partial\:}{\partial\:y}(xy+x^{2})
xy^'=y+x^2sin(x),y(pi/4)=0	xy^{\prime\:}=y+x^{2}\sin(x),y(\frac{π}{4})=0
derivative of 1/2 e^{1/2 x}	\frac{d}{dx}(\frac{1}{2}e^{\frac{1}{2}x})
limit as x approaches+3 of 8/(x-3)	\lim\:_{x\to\:+3}(\frac{8}{x-3})
area 5x, 5/x ,0,5	area\:5x,\frac{5}{x},0,5
integral from 0 to pi/4 of 6tan^3(x)	\int\:_{0}^{\frac{π}{4}}6\tan^{3}(x)dx
(\partial)/(\partial y)((2x-y+5)^2)	\frac{\partial\:}{\partial\:y}((2x-y+5)^{2})
derivative of f(x)=(4x^2-5x)e^x	derivative\:f(x)=(4x^{2}-5x)e^{x}
integral of 5e^{-4x}	\int\:5e^{-4x}dx
derivative of arcsin(9/(x^2))	\frac{d}{dx}(\arcsin(\frac{9}{x^{2}}))
derivative of ((4x)/(x^2+1))^{1/4}	derivative\:(\frac{4x}{x^{2}+1})^{\frac{1}{4}}
derivative of f(x)=4x+2	derivative\:f(x)=4x+2
integral of ((y))/((1+y^{(2)))}	\int\:\frac{(y)}{(1+y^{(2)})}dy
y^{''}+y^'-6y=0,y(0)=2,y^'(0)=-1	y^{\prime\:\prime\:}+y^{\prime\:}-6y=0,y(0)=2,y^{\prime\:}(0)=-1
(5t+2y+6)dt-dy=0	(5t+2y+6)dt-dy=0
derivative of (dy/(dx))+1=0	\frac{d}{dx}(\frac{dy}{dx})+1=0
integral of sqrt((x^3+1)/(x^3)) 1/(x^4)	\int\:\sqrt{\frac{x^{3}+1}{x^{3}}}\frac{1}{x^{4}}dx
f(y)=ln(y)	f(y)=\ln(y)
integral from 0 to sqrt(ln(pi) of)2xe^{x^2}sin(e^{x^2})	\int\:_{0}^{\sqrt{\ln(π)}}2xe^{x^{2}}\sin(e^{x^{2}})dx
derivative of ln((tan(sqrt(x))^3))	\frac{d}{dx}(\ln((\tan(\sqrt{x}))^{3}))
derivative of x^2-5x-6	\frac{d}{dx}(x^{2}-5x-6)
d/(du)((u-sqrt(u))(u+sqrt(u)))	\frac{d}{du}((u-\sqrt{u})(u+\sqrt{u}))
(\partial)/(\partial x)(1/(1-x/a-y/b))	\frac{\partial\:}{\partial\:x}(\frac{1}{1-\frac{x}{a}-\frac{y}{b}})
integral of 1/12 x	\int\:\frac{1}{12}xdx
derivative of sin(0.5x)	derivative\:\sin(0.5x)
y^'=x+8y	y^{\prime\:}=x+8y
(dy)/(dt)-y=1,y(0)=1	\frac{dy}{dt}-y=1,y(0)=1
integral of 1/(25-4x^2)	\int\:\frac{1}{25-4x^{2}}dx

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