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Popular Calculus Problems

derivative of sqrt(2x^2+4x+7)	\frac{d}{dx}(\sqrt{2x^{2}+4x+7})
(\partial)/(\partial x)(sqrt(5x^2+3y^2))	\frac{\partial\:}{\partial\:x}(\sqrt{5x^{2}+3y^{2}})
derivative of f(x)=(\sqrt[3]{t})/(t-6)	derivative\:f(x)=\frac{\sqrt[3]{t}}{t-6}
integral of y/((1+y^2)^{1/2)}	\int\:\frac{y}{(1+y^{2})^{\frac{1}{2}}}dy
integral of (xsin(x^2))	\int\:(x\sin(x^{2}))dx
integral from 1 to 4 of 3/(t^4)	\int\:_{1}^{4}\frac{3}{t^{4}}dt
y^{''}-2y^'+y=0,y(0)=3,y^'(0)=0	y^{\prime\:\prime\:}-2y^{\prime\:}+y=0,y(0)=3,y^{\prime\:}(0)=0
integral from 0 to 1 of 2pix\sqrt[3]{x}	\int\:_{0}^{1}2πx\sqrt[3]{x}dx
derivative of 8x^52pi	\frac{d}{dx}(8x^{5}2π)
integral from 1 to 4 of (x^2+4)/x	\int\:_{1}^{4}\frac{x^{2}+4}{x}dx
derivative of (x^2+6/((2x-7)^7))	\frac{d}{dx}(\frac{x^{2}+6}{(2x-7)^{7}})
limit as x approaches 0 of (200pi)/x	\lim\:_{x\to\:0}(\frac{200π}{x})
normal of y=(y+5x)/(3y-x),(1,2)	normal\:y=\frac{y+5x}{3y-x},(1,2)
derivative of e^{2tan(sqrt(x)})	\frac{d}{dx}(e^{2\tan(\sqrt{x})})
derivative of sqrt(1+t)	derivative\:\sqrt{1+t}
integral of (2x+3)e^{2x}	\int\:(2x+3)e^{2x}dx
d/(dt)(e^{2t}cos(4t))	\frac{d}{dt}(e^{2t}\cos(4t))
derivative of f(x)=(x^4)sqrt(x^2+2)	derivative\:f(x)=(x^{4})\sqrt{x^{2}+2}
integral of (48x)/((x+1)^2(3x+1))	\int\:\frac{48x}{(x+1)^{2}(3x+1)}dx
t^2y^{''}-t(t+2)y^'+(t+2)y=0	t^{2}y^{\prime\:\prime\:}-t(t+2)y^{\prime\:}+(t+2)y=0
tangent of y=4x^2+3x(-3.27)	tangent\:y=4x^{2}+3x(-3.27)
limit as x approaches 2 of ((x+2))/(x-2)	\lim\:_{x\to\:2}(\frac{(x+2)}{x-2})
d/(dy)(1/3 (y^2+2)^{3/2})	\frac{d}{dy}(\frac{1}{3}(y^{2}+2)^{\frac{3}{2}})
integral of cos(2)	\int\:\cos(2)dx
integral of cos^4(x)sin^2(x)	\int\:\cos^{4}(x)\sin^{2}(x)dx
integral from 0 to 3 of sin(x^2)	\int\:_{0}^{3}\sin(x^{2})dx
(dy)/(dx)=y^2+y	\frac{dy}{dx}=y^{2}+y
derivative of y=arccos(x)	derivative\:y=\arccos(x)
limit as x approaches pi of sin(5/3 x)	\lim\:_{x\to\:π}(\sin(\frac{5}{3}x))
(\partial)/(\partial y)(xyz+xy^4+yz^4+zx^4)	\frac{\partial\:}{\partial\:y}(xyz+xy^{4}+yz^{4}+zx^{4})
inverse oflaplace 3/(s^2+2s+1)	inverselaplace\:\frac{3}{s^{2}+2s+1}
tangent of y=-x^3,(1,-1)	tangent\:y=-x^{3},(1,-1)
integral of (arctan(x))/x	\int\:\frac{\arctan(x)}{x}dx
integral of (6ln(x))/x	\int\:\frac{6\ln(x)}{x}dx
derivative of 1/(9+x^2)	\frac{d}{dx}(\frac{1}{9+x^{2}})
integral of x^2(1-x)^5	\int\:x^{2}(1-x)^{5}dx
integral of (x^3)/(sqrt(x^2+2x+5))	\int\:\frac{x^{3}}{\sqrt{x^{2}+2x+5}}dx
d/(dt)(-e^{-t^2})	\frac{d}{dt}(-e^{-t^{2}})
area y=x^2,y=4,x=0	area\:y=x^{2},y=4,x=0
integral from 0 to 7 of pi(2sqrt(5y))^2	\int\:_{0}^{7}π(2\sqrt{5y})^{2}dy
(dy)/(dx)=sin(x-y)	\frac{dy}{dx}=\sin(x-y)
integral of sin(x)cos(x)sqrt(2-cos^2(x))	\int\:\sin(x)\cos(x)\sqrt{2-\cos^{2}(x)}dx
integral of (e^s-e^{-s})^2	\int\:(e^{s}-e^{-s})^{2}ds
derivative of (5-x^2)/((5+x^2)^2)	derivative\:\frac{5-x^{2}}{(5+x^{2})^{2}}
derivative of 3x^{3/2}-1	\frac{d}{dx}(3x^{\frac{3}{2}}-1)
integral of (36)/(x^3)	\int\:\frac{36}{x^{3}}dx
limit as x approaches 1 of 9	\lim\:_{x\to\:1}(9)
integral of sin(5x)cos(7x)	\int\:\sin(5x)\cos(7x)dx
area 5/x , 5/(x^2),1,4	area\:\frac{5}{x},\frac{5}{x^{2}},1,4
slope of y=-3x+2,x=2	slope\:y=-3x+2,x=2
integral of ((x+9)/(sqrt(x)))	\int\:(\frac{x+9}{\sqrt{x}})dx
y^{''}+2y^'+y=3e^{-x}sqrt(x+1)	y^{\prime\:\prime\:}+2y^{\prime\:}+y=3e^{-x}\sqrt{x+1}
f(t)=ln(t^2+1)	f(t)=\ln(t^{2}+1)
sum from n=6 to infinity of e^{3-2n}	\sum\:_{n=6}^{\infty\:}e^{3-2n}
x^2y^{''}+xy^'=0	x^{2}y^{\prime\:\prime\:}+xy^{\prime\:}=0
derivative of 3x^2log_{3}(x)	\frac{d}{dx}(3x^{2}\log_{3}(x))
limit as k approaches 0 of (x^2k+3xk^2+k^2)/(2xk+5k^2)	\lim\:_{k\to\:0}(\frac{x^{2}k+3xk^{2}+k^{2}}{2xk+5k^{2}})
integral of sin^7(x/9)cos(x/9)	\int\:\sin^{7}(\frac{x}{9})\cos(\frac{x}{9})dx
integral of ln(3x+1)	\int\:\ln(3x+1)dx
tangent of f(x)=x^3-7x^2	tangent\:f(x)=x^{3}-7x^{2}
(dy)/(dx)=(e^x+10)^2	\frac{dy}{dx}=(e^{x}+10)^{2}
(\partial}{\partial x}(\frac{(x-y))/z)	\frac{\partial\:}{\partial\:x}(\frac{(x-y)}{z})
integral of (sin(x)e^{2x})	\int\:(\sin(x)e^{2x})dx
derivative of sin(5/x)	\frac{d}{dx}(\sin(\frac{5}{x}))
(\partial)/(\partial x)(xcos(z))	\frac{\partial\:}{\partial\:x}(x\cos(z))
derivative of 4x-5x^{9/10}	\frac{d}{dx}(4x-5x^{\frac{9}{10}})
(3t)^'	(3t)^{\prime\:}
area 2x^2,8x^2,5-3x,0	area\:2x^{2},8x^{2},5-3x,0
(\partial)/(\partial x)(2/(3x+2y))	\frac{\partial\:}{\partial\:x}(\frac{2}{3x+2y})
integral of 9/(sqrt(1+x^2))	\int\:\frac{9}{\sqrt{1+x^{2}}}dx
derivative of (3x^2/(ln(x)))	\frac{d}{dx}(\frac{3x^{2}}{\ln(x)})
(dy)/(dx)=(x+y)^2-1,y(3)=4	\frac{dy}{dx}=(x+y)^{2}-1,y(3)=4
integral from 0 to 1 of 2(1+sqrt(x))^8	\int\:_{0}^{1}2(1+\sqrt{x})^{8}dx
derivative of ((x+2))/((x-2))	derivative\:\frac{(x+2)}{(x-2)}
limit as x approaches 3 of (2^x-8)/(3-x)	\lim\:_{x\to\:3}(\frac{2^{x}-8}{3-x})
area y=4x,y=4,y= 4/9 x^24	area\:y=4x,y=4,y=\frac{4}{9}x^{2}4
integral from 6 to 8 of (62)/((x-6)^3)	\int\:_{6}^{8}\frac{62}{(x-6)^{3}}dx
(\partial)/(\partial u)(u^2v)	\frac{\partial\:}{\partial\:u}(u^{2}v)
integral of 12x^3(ln(4x))^2	\int\:12x^{3}(\ln(4x))^{2}dx
integral of (3x^2+8)	\int\:(3x^{2}+8)dx
y^'=(1-2t)/y	y^{\prime\:}=\frac{1-2t}{y}
derivative of (x^2+10^6)	\frac{d}{dx}((x^{2}+10)^{6})
limit as x approaches 0 of (sin(6x^2))/(1-cos(3x))	\lim\:_{x\to\:0}(\frac{\sin(6x^{2})}{1-\cos(3x)})
integral of (1+x^2)^{-2}	\int\:(1+x^{2})^{-2}dx
(x^6)^'	(x^{6})^{\prime\:}
derivative of sqrt(9+x^2)	\frac{d}{dx}(\sqrt{9+x^{2}})
derivative of e^{x^4y}	\frac{d}{dx}(e^{x^{4}y})
integral of x^3(5+x^4)^{11}	\int\:x^{3}(5+x^{4})^{11}dx
integral from x^3 to x^4 of (2t-1)^3	\int\:_{x^{3}}^{x^{4}}(2t-1)^{3}dt
integral of (sqrt(3))	\int\:(\sqrt{3})dx
derivative of f(x)=(60)/(0.01x^2+1)	derivative\:f(x)=\frac{60}{0.01x^{2}+1}
derivative of arctan(x^2+1)	\frac{d}{dx}(\arctan(x^{2}+1))
sum from n=1 to infinity of (50)/(5^n)	\sum\:_{n=1}^{\infty\:}\frac{50}{5^{n}}
derivative of e^{ln(sec(2x))}	derivative\:e^{\ln(\sec(2x))}
derivative of (sin(2x)/2)	\frac{d}{dx}(\frac{\sin(2x)}{2})
y^{''}-5y^'+6y=xe^x	y^{\prime\:\prime\:}-5y^{\prime\:}+6y=xe^{x}
integral of (e^{6x})/(e^{6x)-3e^{-6x}}	\int\:\frac{e^{6x}}{e^{6x}-3e^{-6x}}dx
integral of (8y)/x	\int\:\frac{8y}{x}dx
limit as x approaches infinity of (3.4)/(0.1+33.9e^{-0.5678x)}	\lim\:_{x\to\:\infty\:}(\frac{3.4}{0.1+33.9e^{-0.5678x}})
laplacetransform t^31(t)	laplacetransform\:t^{3}1(t)

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