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Popular Calculus Problems

(dy)/(dt)+(3t)/(t^2+1)y=(6t)/(t^2+1)	\frac{dy}{dt}+\frac{3t}{t^{2}+1}y=\frac{6t}{t^{2}+1}
integral of-3x^4	\int\:-3x^{4}dx
derivative of (2x-1/(x+9))	\frac{d}{dx}(\frac{2x-1}{x+9})
area (x-1)^3,x-1,0,1	area\:(x-1)^{3},x-1,0,1
integral from 0 to 2 of 2piy(4-y^2)	\int\:_{0}^{2}2πy(4-y^{2})dy
derivative of (x+1/(x-2))	\frac{d}{dx}(\frac{x+1}{x-2})
integral of 3/(x^6)	\int\:\frac{3}{x^{6}}dx
tangent of y=x^2-2x-2,(3,1)	tangent\:y=x^{2}-2x-2,(3,1)
integral of 1/2 (3sin(x)+7)	\int\:\frac{1}{2}(3\sin(x)+7)dx
derivative of y=2x(5-3x)^4	derivative\:y=2x(5-3x)^{4}
limit as x approaches 0 of (sec(x))/x	\lim\:_{x\to\:0}(\frac{\sec(x)}{x})
area x^2+2,2x+5	area\:x^{2}+2,2x+5
x^2y^{''}+2xy^'-12y=0	x^{2}y^{\prime\:\prime\:}+2xy^{\prime\:}-12y=0
derivative of cos(e^{sqrt(tan(2x)}))	\frac{d}{dx}(\cos(e^{\sqrt{\tan(2x)}}))
integral of-1/2 e^ysin(2y)	\int\:-\frac{1}{2}e^{y}\sin(2y)dy
(\partial)/(\partial x)(42x^5y^6-30x^4y^5)	\frac{\partial\:}{\partial\:x}(42x^{5}y^{6}-30x^{4}y^{5})
x^2y^{''}-5xy^'-7y=0	x^{2}y^{\prime\:\prime\:}-5xy^{\prime\:}-7y=0
y^'=-5cos(3x)y	y^{\prime\:}=-5\cos(3x)y
derivative of f(x)=e^{-6x}	derivative\:f(x)=e^{-6x}
(\partial)/(\partial x)(x^9-7y)	\frac{\partial\:}{\partial\:x}(x^{9}-7y)
integral of e^{1.2x}	\int\:e^{1.2x}dx
derivative of 4-sqrt(x+16)	derivative\:4-\sqrt{x+16}
integral of 1/(x^2sqrt(5+x^2))	\int\:\frac{1}{x^{2}\sqrt{5+x^{2}}}dx
derivative of 5pi^6	derivative\:5π^{6}
limit as x approaches 0-of arctan(ln(x))	\lim\:_{x\to\:0-}(\arctan(\ln(x)))
(\partial)/(\partial y)(tan(2+2x^2y^3z^2))	\frac{\partial\:}{\partial\:y}(\tan(2+2x^{2}y^{3}z^{2}))
integral of x^{7/6}	\int\:x^{\frac{7}{6}}dx
integral from-1 to 2 of 5	\int\:_{-1}^{2}5dx
(dy)/(dx)+7(tan(7x))y=9cos(7x)	\frac{dy}{dx}+7(\tan(7x))y=9\cos(7x)
derivative of arccos(7x^2)	\frac{d}{dx}(\arccos(7x^{2}))
integral of (x^2+8x-4)/(x^3-4x)	\int\:\frac{x^{2}+8x-4}{x^{3}-4x}dx
(\partial)/(\partial y)(2x-y/x)	\frac{\partial\:}{\partial\:y}(2x-\frac{y}{x})
derivative of (x^2-4/(x+0.5))	\frac{d}{dx}(\frac{x^{2}-4}{x+0.5})
limit as y approaches 0 of ax^2+bx^3	\lim\:_{y\to\:0}(ax^{2}+bx^{3})
derivative of f(x)=2e^x(cos(x)-sin(x))	derivative\:f(x)=2e^{x}(\cos(x)-\sin(x))
30y^{''}+19y^'-5y=0	30y^{\prime\:\prime\:}+19y^{\prime\:}-5y=0
slope ofintercept (3,4),(5,-4)	slopeintercept\:(3,4),(5,-4)
(dy}{dx}=\frac{-xe^{-x^2})/y	\frac{dy}{dx}=\frac{-xe^{-x^{2}}}{y}
tangent of y=(x-4)/(x-5),(6,2)	tangent\:y=\frac{x-4}{x-5},(6,2)
derivative of e^{x-5}	\frac{d}{dx}(e^{x-5})
integral of (5e^{2x})/(e^{2x)+11e^x+24}	\int\:\frac{5e^{2x}}{e^{2x}+11e^{x}+24}dx
(dy)/(dx)+6y=7	\frac{dy}{dx}+6y=7
(\partial)/(\partial x)(xycos(z))	\frac{\partial\:}{\partial\:x}(xy\cos(z))
integral of-xe^{y/x}	\int\:-xe^{\frac{y}{x}}
derivative of x^2+5x+4	\frac{d}{dx}(x^{2}+5x+4)
normal of y=x^2-4x,(3,-3)	normal\:y=x^{2}-4x,(3,-3)
derivative of 9.75+1.5x^3	\frac{d}{dx}(9.75+1.5x^{3})
integral from 0 to 8 of (2x-1)/(x+1)	\int\:_{0}^{8}\frac{2x-1}{x+1}dx
integral of 1/(2x^2-2x+3)	\int\:\frac{1}{2x^{2}-2x+3}dx
d/(dt)(sqrt(t)e^{-t})	\frac{d}{dt}(\sqrt{t}e^{-t})
integral of 1-cos(4x)	\int\:1-\cos(4x)dx
(\partial)/(\partial x)(-x/(y^2+x^2))	\frac{\partial\:}{\partial\:x}(-\frac{x}{y^{2}+x^{2}})
derivative of 2e^{-2x}x-2e^{-2x}x^2	\frac{d}{dx}(2e^{-2x}x-2e^{-2x}x^{2})
(sqrt(4-x^2))^'	(\sqrt{4-x^{2}})^{\prime\:}
derivative of sin(xe^{-cos(x)})	\frac{d}{dx}(\sin(x)e^{-\cos(x)})
limit as x approaches 100000 of x^3+2x+1	\lim\:_{x\to\:100000}(x^{3}+2x+1)
derivative of 2x^2-2x+c	\frac{d}{dx}(2x^{2}-2x+c)
(d^2)/(dx^2)(x(2x+1)^5)	\frac{d^{2}}{dx^{2}}(x(2x+1)^{5})
integral of-4sqrt(x)e^{sqrt(x)}	\int\:-4\sqrt{x}e^{\sqrt{x}}dx
y^'+(tan(x))y=cos(x)	y^{\prime\:}+(\tan(x))y=\cos(x)
derivative of (x^3-3x^2+4/(x^2))	\frac{d}{dx}(\frac{x^{3}-3x^{2}+4}{x^{2}})
inverse oflaplace 1/((s-5)^4)	inverselaplace\:\frac{1}{(s-5)^{4}}
y^'+tan(2*x)y=0	y^{\prime\:}+\tan(2\cdot\:x)y=0
integral of 2x(x^2-2)	\int\:2x(x^{2}-2)dx
normal of f(x)=(x+2)sqrt(2x-3),\at x=2	normal\:f(x)=(x+2)\sqrt{2x-3},\at\:x=2
sum from n=1 to infinity of (pi/5)^n	\sum\:_{n=1}^{\infty\:}(\frac{π}{5})^{n}
area y= 1/x ,y=x,x=3	area\:y=\frac{1}{x},y=x,x=3
derivative of-(4x/(x^2+1))	\frac{d}{dx}(-\frac{4x}{x^{2}+1})
integral of (8-128x)/(sqrt(9-64x^2))	\int\:\frac{8-128x}{\sqrt{9-64x^{2}}}dx
(\partial)/(\partial t)(tcos(s))	\frac{\partial\:}{\partial\:t}(t\cos(s))
derivative of f(x)= 1/(x^2-4)	derivative\:f(x)=\frac{1}{x^{2}-4}
(arccos(x))^'	(\arccos(x))^{\prime\:}
(d^4)/(dx^4)(5e^{x^2})	\frac{d^{4}}{dx^{4}}(5e^{x^{2}})
derivative of x^3-7x^2+15x-10	\frac{d}{dx}(x^{3}-7x^{2}+15x-10)
(6y+2t-9)dt+(8y+6t-1)dy=0	(6y+2t-9)dt+(8y+6t-1)dy=0
integral from 1 to 2 of 6x^23^{x^3}	\int\:_{1}^{2}6x^{2}3^{x^{3}}dx
integral of (ln(t))/(t^2)	\int\:\frac{\ln(t)}{t^{2}}dt
integral of 2e^xsinh(x)	\int\:2e^{x}\sinh(x)dx
derivative of g(y)=-y/((y^2+1)^{3/2)}	derivative\:g(y)=-\frac{y}{(y^{2}+1)^{\frac{3}{2}}}
integral of ln(x^2+15x+44)	\int\:\ln(x^{2}+15x+44)dx
integral of 1/((484+x^2)^{3/2)}	\int\:\frac{1}{(484+x^{2})^{\frac{3}{2}}}dx
inverse oflaplace (3^2)/((s+3)^2)*1/s	inverselaplace\:\frac{3^{2}}{(s+3)^{2}}\cdot\:\frac{1}{s}
integral of (sqrt(1-w))/(sqrt(w))	\int\:\frac{\sqrt{1-w}}{\sqrt{w}}dw
f(x)=sin^2(4x)	f(x)=\sin^{2}(4x)
(\partial)/(\partial v)(2sin(u)cos(v))	\frac{\partial\:}{\partial\:v}(2\sin(u)\cos(v))
area e^x,(e^{2x})/2 ,0,1	area\:e^{x},\frac{e^{2x}}{2},0,1
derivative of-1/(4(x^{3/2)})	\frac{d}{dx}(-\frac{1}{4(x)^{\frac{3}{2}}})
derivative of (4x)/((x^2+1)^2)	derivative\:\frac{4x}{(x^{2}+1)^{2}}
derivative of y=(5x^2+8x+4)/(sqrt(x))	derivative\:y=\frac{5x^{2}+8x+4}{\sqrt{x}}
implicit y=sin(3x+4y)	implicit\:y=\sin(3x+4y)
limit as x approaches 2 of sqrt(x^2+5)	\lim\:_{x\to\:2}(\sqrt{x^{2}+5})
derivative of 5(x^2+2x)^3	derivative\:5(x^{2}+2x)^{3}
derivative of sqrt(x)e^{x^2}(x^2+1)^8	derivative\:\sqrt{x}e^{x^{2}}(x^{2}+1)^{8}
integral of y/(sqrt(3y+5))	\int\:\frac{y}{\sqrt{3y+5}}dy
integral of e^{-2sqrt(x)}2sqrt(x)	\int\:e^{-2\sqrt{x}}2\sqrt{x}dx
derivative of (4x)^{2x}	derivative\:(4x)^{2x}
sum from n=0 to infinity of 1/(n^{1.1)}	\sum\:_{n=0}^{\infty\:}\frac{1}{n^{1.1}}
derivative of 5/(x^3-2/(x^2)-1/x+200)	\frac{d}{dx}(\frac{5}{x^{3}}-\frac{2}{x^{2}}-\frac{1}{x}+200)
derivative of y=-2x^{-4}+4/x-(2x^2)/3	derivative\:y=-2x^{-4}+\frac{4}{x}-\frac{2x^{2}}{3}
derivative of x^2+4x+4	\frac{d}{dx}(x^{2}+4x+4)

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