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Popular Calculus Problems

(2x+3)y^'=y+sqrt(2x+3)	(2x+3)y^{\prime\:}=y+\sqrt{2x+3}
(1dy)/(x^2dx)=y^2+9	\frac{1dy}{x^{2}dx}=y^{2}+9
derivative of 2^{90}	derivative\:2^{90}
derivative of f(x)=2x^2-7x+5	derivative\:f(x)=2x^{2}-7x+5
derivative of (e^{4x^2+1}/8)	\frac{d}{dx}(\frac{e^{4x^{2}+1}}{8})
derivative of-2xsin(2x)	\frac{d}{dx}(-2x\sin(2x))
integral from 0 to pi/3 of sec^3(x)	\int\:_{0}^{\frac{π}{3}}\sec^{3}(x)dx
integral of (x+1)/(sqrt(4-x^2))	\int\:\frac{x+1}{\sqrt{4-x^{2}}}dx
derivative of 5x(sin(x+cos(x)))	\frac{d}{dx}(5x(\sin(x)+\cos(x)))
7x^2y+y^'=6x^2	7x^{2}y+y^{\prime\:}=6x^{2}
y^{'''}-5y^{''}-6y^'=0	y^{\prime\:\prime\:\prime\:}-5y^{\prime\:\prime\:}-6y^{\prime\:}=0
d/(dt)(sqrt(t))	\frac{d}{dt}(\sqrt{t})
xy^'-4y=x	xy^{\prime\:}-4y=x
derivative of f(t)=cos(t)	derivative\:f(t)=\cos(t)
limit as x approaches 0 of (1+7x)^{2/x}	\lim\:_{x\to\:0}((1+7x)^{\frac{2}{x}})
(\partial)/(\partial x)(x^2y^3+4xyz-3yz)	\frac{\partial\:}{\partial\:x}(x^{2}y^{3}+4xyz-3yz)
integral of ((4+x^2)^2)/(x^3)	\int\:\frac{(4+x^{2})^{2}}{x^{3}}dx
laplacetransform 6e^{-3}-t^2+2t-8	laplacetransform\:6e^{-3}-t^{2}+2t-8
xy^'+2y=-2sin(x)	xy^{\prime\:}+2y=-2\sin(x)
integral of (48)/((6x+1)^9)	\int\:\frac{48}{(6x+1)^{9}}dx
integral of 10sin^3(xco)s^7x	\int\:10\sin^{3}(xco)s^{7}xdx
simplify (4x)/(sqrt(x))	simplify\:\frac{4x}{\sqrt{x}}
integral of x/(sqrt(2x-6))	\int\:\frac{x}{\sqrt{2x-6}}dx
4xy^'-20y=x^{-8}	4xy^{\prime\:}-20y=x^{-8}
derivative of (cx^{1/2})	\frac{d}{dx}((cx)^{\frac{1}{2}})
integral of (x^3+64)/(x^2+64)	\int\:\frac{x^{3}+64}{x^{2}+64}dx
limit as t approaches 2-of-(3t)/(t-2)	\lim\:_{t\to\:2-}(-\frac{3t}{t-2})
limit as x approaches 1+of 3/(x^2-1)	\lim\:_{x\to\:1+}(\frac{3}{x^{2}-1})
derivative of 11x^2e^x	derivative\:11x^{2}e^{x}
tangent of 4x^2	tangent\:4x^{2}
sum from n=0 to infinity of (e^n)/((n!))	\sum\:_{n=0}^{\infty\:}\frac{e^{n}}{(n!)}
integral of (e^{4x})	\int\:(e^{4x})dx
(\partial)/(\partial x)(+4x-5+6xy)	\frac{\partial\:}{\partial\:x}(+4x-5+6xy)
(d^2x)/(dt^2)=5+2x	\frac{d^{2}x}{dt^{2}}=5+2x
(dN)/(dt)+N=Nte^{t+3}	\frac{dN}{dt}+N=Nte^{t+3}
derivative of sqrt(5x+6)	derivative\:\sqrt{5x+6}
derivative of x+y	derivative\:x+y
integral of (1-sqrt(x))/(1+sqrt(x))	\int\:\frac{1-\sqrt{x}}{1+\sqrt{x}}dx
derivative of 1/(2sqrt(x))+1/(3x^{2/3)}	derivative\:\frac{1}{2\sqrt{x}}+\frac{1}{3x^{\frac{2}{3}}}
derivative of (8x^3-6x^2/(x^2+3x-2))	\frac{d}{dx}(\frac{8x^{3}-6x^{2}}{x^{2}+3x-2})
laplacetransform 3cos(4t)	laplacetransform\:3\cos(4t)
integral of e^{2/x}	\int\:e^{\frac{2}{x}}dx
integral of 10x+3x^2+12x^3+C	\int\:10x+3x^{2}+12x^{3}+Cdx
inverse oflaplace ((s+1))/(s^2+2s+2)	inverselaplace\:\frac{(s+1)}{s^{2}+2s+2}
limit as h approaches 0 of h-9/h+4	\lim\:_{h\to\:0}(h-\frac{9}{h}+4)
integral of (x^2-5x+2)/(3sqrt(x))	\int\:\frac{x^{2}-5x+2}{3\sqrt{x}}dx
tangent of f(x)=-2x^3+x^2,\at x=1	tangent\:f(x)=-2x^{3}+x^{2},\at\:x=1
tangent of y=sqrt(10x),(10,10)	tangent\:y=\sqrt{10x},(10,10)
derivative of ln(5-x^2)	\frac{d}{dx}(\ln(5-x^{2}))
integral from 2 to 4 of 1/(sqrt(16-t^2))	\int\:_{2}^{4}\frac{1}{\sqrt{16-t^{2}}}dt
limit as x approaches 2 of 2x-2	\lim\:_{x\to\:2}(2x-2)
integral of (x^3)/(x^2-2x+4)	\int\:\frac{x^{3}}{x^{2}-2x+4}dx
integral of (sec(sqrt(x)))/(sqrt(x))	\int\:\frac{\sec(\sqrt{x})}{\sqrt{x}}dx
y^{''}-2y^'-3y=-3te^{-t}	y^{\prime\:\prime\:}-2y^{\prime\:}-3y=-3te^{-t}
limit as x approaches 1 of x-2	\lim\:_{x\to\:1}(x-2)
limit as x approaches infinity of (2^{x+1})/(3^{x-1)}	\lim\:_{x\to\:\infty\:}(\frac{2^{x+1}}{3^{x-1}})
integral of x^2sin(4x)	\int\:x^{2}\sin(4x)dx
derivative of (x^5-9)sqrt(x)	derivative\:(x^{5}-9)\sqrt{x}
derivative of csc^3(x)	\frac{d}{dx}(\csc^{3}(x))
integral of pi(sqrt(x))^2	\int\:π(\sqrt{x})^{2}dx
integral from-1 to 2 of sqrt(1+4x^2)	\int\:_{-1}^{2}\sqrt{1+4x^{2}}dx
derivative of f(x)=5x^2-2x	derivative\:f(x)=5x^{2}-2x
limit as x approaches infinity of x^3+4x	\lim\:_{x\to\:\infty\:}(x^{3}+4x)
integral of 49e^{-7x}sin(7x)	\int\:49e^{-7x}\sin(7x)dx
(\partial)/(\partial x)(cos(6y-2x))	\frac{\partial\:}{\partial\:x}(\cos(6y-2x))
(\partial)/(\partial x)(y^6cos(6x)*6)	\frac{\partial\:}{\partial\:x}(y^{6}\cos(6x)\cdot\:6)
derivative of y= 1/((7x+16)^4)	derivative\:y=\frac{1}{(7x+16)^{4}}
derivative of 7sec(x)	derivative\:7\sec(x)
(\partial)/(\partial x)(y/(y-4x))	\frac{\partial\:}{\partial\:x}(\frac{y}{y-4x})
derivative of ((e^x))/(1+x)	derivative\:\frac{(e^{x})}{1+x}
limit as x approaches infinity of (x^4)/(e^{-6x)}	\lim\:_{x\to\:\infty\:}(\frac{x^{4}}{e^{-6x}})
area y=2ln(x),y=0,x=3e	area\:y=2\ln(x),y=0,x=3e
integral from 1 to-2 of (1/2)	\int\:_{1}^{-2}(\frac{1}{2})dx
inverse oflaplace 5/(s^2+5)	inverselaplace\:\frac{5}{s^{2}+5}
tangent of f(x)=1+2x-3x^2,\at x=0	tangent\:f(x)=1+2x-3x^{2},\at\:x=0
derivative of (ln(1-x^2)/(x^2))	\frac{d}{dx}(\frac{\ln(1-x^{2})}{x^{2}})
derivative of x^5+1	\frac{d}{dx}(x^{5}+1)
integral of (cot(ln(x^4+1))x^3)/(x^4+1)	\int\:\frac{\cot(\ln(x^{4}+1))x^{3}}{x^{4}+1}dx
inverse oflaplace ((s^2+1))/(s(s-1)^3)	inverselaplace\:\frac{(s^{2}+1)}{s(s-1)^{3}}
(\partial)/(\partial x)(e^{xy+1})	\frac{\partial\:}{\partial\:x}(e^{xy+1})
maclaurin ((5x-2))/((x+1)),4	maclaurin\:\frac{(5x-2)}{(x+1)},4
derivative of (2x^3-3(sin(x)+2))	\frac{d}{dx}((2x^{3}-3)(\sin(x)+2))
area 3cos(x),3cos(2x),0<= x<= pi	area\:3\cos(x),3\cos(2x),0\le\:x\le\:π
(1+y^2sin(2x))dx-2ycos^2(x)dy=0	(1+y^{2}\sin(2x))dx-2y\cos^{2}(x)dy=0
(dy)/(dx)=xy^3	\frac{dy}{dx}=xy^{3}
integral of 1/(x^2+12)	\int\:\frac{1}{x^{2}+12}dx
area 3x,9x^2	area\:3x,9x^{2}
sum from n=1 to infinity of (2n)/(11^n)	\sum\:_{n=1}^{\infty\:}\frac{2n}{11^{n}}
(dy)/(dx)=3+e^{(-3x+y+4)}	\frac{dy}{dx}=3+e^{(-3x+y+4)}
(\partial)/(\partial x)(x^2+xy^3)	\frac{\partial\:}{\partial\:x}(x^{2}+xy^{3})
derivative of (4sqrt(2)/3 x^{3/2}-1)	\frac{d}{dx}(\frac{4\sqrt{2}}{3}x^{\frac{3}{2}}-1)
derivative of-1/(sin(x))	\frac{d}{dx}(-\frac{1}{\sin(x)})
y^{''}+3y^'=sin(t),y(0)=1,y^'(0)=2	y^{\prime\:\prime\:}+3y^{\prime\:}=\sin(t),y(0)=1,y^{\prime\:}(0)=2
integral of sec(x)+tan(x)	\int\:\sec(x)+\tan(x)dx
integral of x^3sqrt(x^4-1)	\int\:x^{3}\sqrt{x^{4}-1}dx
derivative of (1-x^{2/3})^{3/2}	derivative\:(1-x^{\frac{2}{3}})^{\frac{3}{2}}
derivative of 3/2 sin(x)	\frac{d}{dx}(\frac{3}{2}\sin(x))
integral of (sqrt(1-x))/(sqrt(x))	\int\:\frac{\sqrt{1-x}}{\sqrt{x}}dx
integral of 3(x-1)^2	\int\:3(x-1)^{2}dx
integral of 3x^2y+4xy^2	\int\:3x^{2}y+4xy^{2}dx

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