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Popular Calculus Problems

y^'+2xy=xy^2	y^{\prime\:}+2xy=xy^{2}
(\partial)/(\partial x)(3e^xsin(y))	\frac{\partial\:}{\partial\:x}(3e^{x}\sin(y))
tangent of f(x)=sqrt(x-2),\at x=9	tangent\:f(x)=\sqrt{x-2},\at\:x=9
laplacetransform 6*cos(0.2t)	laplacetransform\:6\cdot\:\cos(0.2t)
(dy)/(dx)=3y+2	\frac{dy}{dx}=3y+2
limit as x approaches 1 of sin(pi/2 x)	\lim\:_{x\to\:1}(\sin(\frac{π}{2}x))
tangent of f(x)=4sqrt(x),\at x=4	tangent\:f(x)=4\sqrt{x},\at\:x=4
integral of-(cos(x))/(sin(x))	\int\:-\frac{\cos(x)}{\sin(x)}dx
integral of cos(pint)	\int\:\cos(πnt)dt
sum from n=1 to infinity of (pi/6)^n	\sum\:_{n=1}^{\infty\:}(\frac{π}{6})^{n}
derivative of (tan(x))^{3/x}	derivative\:(\tan(x))^{\frac{3}{x}}
y^{''}-y^'+1/4 y=7+e^{x/2}	y^{\prime\:\prime\:}-y^{\prime\:}+\frac{1}{4}y=7+e^{\frac{x}{2}}
integral of sqrt(t)(t^6+t-5)	\int\:\sqrt{t}(t^{6}+t-5)dt
limit as x approaches infinity of 3e^{-3x}	\lim\:_{x\to\:\infty\:}(3e^{-3x})
derivative of f(x)=(x^3-5x)(5x^2+3x)	derivative\:f(x)=(x^{3}-5x)(5x^{2}+3x)
(\partial)/(\partial x)([Ax^2+By^3]^{1/4})	\frac{\partial\:}{\partial\:x}([Ax^{2}+By^{3}]^{\frac{1}{4}})
integral of sqrt(24+10x-x^2)	\int\:\sqrt{24+10x-x^{2}}dx
derivative of 6/x-2	\frac{d}{dx}(\frac{6}{x}-2)
integral from 0 to 5 of pi(2sqrt(7y))^2	\int\:_{0}^{5}π(2\sqrt{7y})^{2}dy
integral from 2 to infinity of e^{-9x}	\int\:_{2}^{\infty\:}e^{-9x}dx
integral of 1/(4xy^2)	\int\:\frac{1}{4xy^{2}}dx
derivative of f(x)=(11x+7)/(3x^4+2x^2)	derivative\:f(x)=\frac{11x+7}{3x^{4}+2x^{2}}
(\partial)/(\partial x)((x^2+y^2)/(xy))	\frac{\partial\:}{\partial\:x}(\frac{x^{2}+y^{2}}{xy})
(\partial}{\partial x}(\frac{y^3)/x)	\frac{\partial\:}{\partial\:x}(\frac{y^{3}}{x})
derivative of 3x^2+4x+1	\frac{d}{dx}(3x^{2}+4x+1)
integral of 1/((x+1)(x+3))	\int\:\frac{1}{(x+1)(x+3)}dx
integral of ((2-x)^{1/2})	\int\:((2-x)^{\frac{1}{2}})dx
derivative of f(x)=x^4ln(x)	derivative\:f(x)=x^{4}\ln(x)
tangent of y=7x-x^2(1.6)	tangent\:y=7x-x^{2}(1.6)
tangent of e^x-2x	tangent\:e^{x}-2x
derivative of (2x^2+4x+6/(sqrt(x)))	\frac{d}{dx}(\frac{2x^{2}+4x+6}{\sqrt{x}})
derivative of 4x^2-4x+1	\frac{d}{dx}(4x^{2}-4x+1)
f(x)=arcsin(ln(x))	f(x)=\arcsin(\ln(x))
limit as x approaches 1 of 1-1/(3x-1)	\lim\:_{x\to\:1}(1-\frac{1}{3x-1})
integral of 6/(1-cos(2x))	\int\:\frac{6}{1-\cos(2x)}dx
xy^'=y	xy^{\prime\:}=y
xy^'e^x+2ye^x=0	xy^{\prime\:}e^{x}+2ye^{x}=0
(\partial)/(\partial x)(ln(x^3+y))	\frac{\partial\:}{\partial\:x}(\ln(x^{3}+y))
tangent of-3x^2,\at x=2	tangent\:-3x^{2},\at\:x=2
integral of (3x+5)^2	\int\:(3x+5)^{2}dx
derivative of x^2-3x-5x^{-1}+7x^{-2}	\frac{d}{dx}(x^{2}-3x-5x^{-1}+7x^{-2})
(dy)/(dx)=(x^2-3)/(6y^2)	\frac{dy}{dx}=\frac{x^{2}-3}{6y^{2}}
integral from 0 to 1 of x/(x+1)	\int\:_{0}^{1}\frac{x}{x+1}dx
integral of (2t)^{-1/2}	\int\:(2t)^{-\frac{1}{2}}dt
integral from-2 to sin(x) of 3t	\int\:_{-2}^{\sin(x)}3tdt
integral from 0 to 1 of 2/3 (x+2y)	\int\:_{0}^{1}\frac{2}{3}(x+2y)dx
derivative of ax+cot(ax)	\frac{d}{dx}(ax+\cot(ax))
y^{''}+16y=40sec(4t)	y^{\prime\:\prime\:}+16y=40\sec(4t)
limit as x approaches-4+of (-4x)/(x+4)	\lim\:_{x\to\:-4+}(\frac{-4x}{x+4})
f(x)=2sin^2(x)	f(x)=2\sin^{2}(x)
(\partial)/(\partial x)(7ye^x)	\frac{\partial\:}{\partial\:x}(7ye^{x})
(dy)/(dx)=(2x+sec^2(x))/(2y),y(0)=-7	\frac{dy}{dx}=\frac{2x+\sec^{2}(x)}{2y},y(0)=-7
derivative of ((2x^5+3x^4-x^3+2)/(x^2))	\frac{d}{dx}(\frac{(2x^{5}+3x^{4}-x^{3}+2)}{x^{2}})
factor 12x^2-12x-2	factor\:12x^{2}-12x-2
integral of 1/(1+(1+x^2)^{1/2)}	\int\:\frac{1}{1+(1+x^{2})^{\frac{1}{2}}}dx
derivative of ln(x^2-9)	\frac{d}{dx}(\ln(x^{2}-9))
integral of 6xln(3x)	\int\:6x\ln(3x)dx
derivative of-3x-2	\frac{d}{dx}(-3x-2)
integral of x(sqrt(x)+2)	\int\:x(\sqrt{x}+2)dx
integral of (e^xsqrt(e^x-1))/(e^x+3)	\int\:\frac{e^{x}\sqrt{e^{x}-1}}{e^{x}+3}dx
(dy)/(dx)= 1/(x^2+1)-1/(sqrt(1-x^2))	\frac{dy}{dx}=\frac{1}{x^{2}+1}-\frac{1}{\sqrt{1-x^{2}}}
sum from n=1 to infinity of (1/8)^n	\sum\:_{n=1}^{\infty\:}(\frac{1}{8})^{n}
derivative of (x+3/(x^3+x-2))	\frac{d}{dx}(\frac{x+3}{x^{3}+x-2})
integral of 1/((8x-1)^3)	\int\:\frac{1}{(8x-1)^{3}}dx
integral of (2x^2-1)/((4x-1)(x^2+1))	\int\:\frac{2x^{2}-1}{(4x-1)(x^{2}+1)}dx
derivative of f(x)=a^2	derivative\:f(x)=a^{2}
derivative of (x^2-49)/(x-7)	derivative\:\frac{x^{2}-49}{x-7}
derivative of f(x)=4x-3x^2	derivative\:f(x)=4x-3x^{2}
(y-2)dy+xdx=0	(y-2)dy+xdx=0
area y=sqrt(x+2),y= 1/(x+1),[0,2]	area\:y=\sqrt{x+2},y=\frac{1}{x+1},[0,2]
derivative of 5x^3+3x	\frac{d}{dx}(5x^{3}+3x)
(\partial)/(\partial x)((x^3+5)/(y^3-1))	\frac{\partial\:}{\partial\:x}(\frac{x^{3}+5}{y^{3}-1})
derivative of arccos(e^{3x})	\frac{d}{dx}(\arccos(e^{3x}))
derivative of 1/(sqrt(x^3))	derivative\:\frac{1}{\sqrt{x^{3}}}
integral of sec(x)tan(x)-4x	\int\:\sec(x)\tan(x)-4xdx
integral of (x^4+5)^3x^3	\int\:(x^{4}+5)^{3}x^{3}dx
derivative of cos^2(xsin^2(x))	\frac{d}{dx}(\cos^{2}(x)\sin^{2}(x))
integral of 9rcos(r)	\int\:9r\cos(r)dr
derivative of y=x^{4x}	derivative\:y=x^{4x}
(dy)/(dx)=(y^2-4)	\frac{dy}{dx}=(y^{2}-4)
limit as x approaches-2 of sqrt(x+1)	\lim\:_{x\to\:-2}(\sqrt{x+1})
sum from n=1 to infinity of 1*(1/5)^n	\sum\:_{n=1}^{\infty\:}1\cdot\:(\frac{1}{5})^{n}
integral of e^xsqrt(23+e^x)	\int\:e^{x}\sqrt{23+e^{x}}dx
derivative of y=6tan(x/3)cos(7x)	derivative\:y=6\tan(\frac{x}{3})\cos(7x)
derivative of t^3-3t	derivative\:t^{3}-3t
derivative of (4z+e^{-z^2})^3	derivative\:(4z+e^{-z^{2}})^{3}
integral of 2/(e^{2x)}	\int\:\frac{2}{e^{2x}}dx
integral of 100	\int\:100dx
integral from 0 to 2pi of sin^2(12x)	\int\:_{0}^{2π}\sin^{2}(12x)dx
limit as x approaches infinity of e^{-3x}cos(3x)	\lim\:_{x\to\:\infty\:}(e^{-3x}\cos(3x))
integral of e^{-st}t^2	\int\:e^{-st}t^{2}dt
integral of x/(e^{2x)}	\int\:\frac{x}{e^{2x}}dx
integral of 1/((x^2+b^2)^{3/2)}	\int\:\frac{1}{(x^{2}+b^{2})^{\frac{3}{2}}}dx
limit as x approaches (-1+1) of 1/(x-2)	\lim\:_{x\to\:(-1+1)}(\frac{1}{x-2})
tangent of y=2x^3-2x,(-1,0)	tangent\:y=2x^{3}-2x,(-1,0)
integral of xcos(x)+cos(x)-1	\int\:x\cos(x)+\cos(x)-1dx
integral of sqrt(cos^2(x)-sin^2(x))	\int\:\sqrt{\cos^{2}(x)-\sin^{2}(x)}dx
laplacetransform (t-3)^4	laplacetransform\:(t-3)^{4}
derivative of e^{2x}+5	\frac{d}{dx}(e^{2x}+5)
(2xy^2-7)dx+(2x^2y+5)dy=0	(2xy^{2}-7)dx+(2x^{2}y+5)dy=0

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