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Popular Calculus Problems

derivative of f(x)=(120x^2)/(x^2+4)	derivative\:f(x)=\frac{120x^{2}}{x^{2}+4}
limit as x approaches pi/2-of tan(x)	\lim\:_{x\to\:\frac{π}{2}-}(\tan(x))
derivative of sqrt(7x^3-7x^2-(9/x))	derivative\:\sqrt{7x^{3}-7x^{2}-(\frac{9}{x})}
(\partial)/(\partial x)(-xy(3-x-y))	\frac{\partial\:}{\partial\:x}(-xy(3-x-y))
sum from n=1 to infinity of (3n)/(2n+9)	\sum\:_{n=1}^{\infty\:}\frac{3n}{2n+9}
integral of 4sec^2(x)	\int\:4\sec^{2}(x)dx
derivative of \sqrt[x]{e}	\frac{d}{dx}(\sqrt[x]{e})
integral of 8/(sec(2x)-1)	\int\:\frac{8}{\sec(2x)-1}dx
(\partial)/(\partial x)(sin(xy)z^2)	\frac{\partial\:}{\partial\:x}(\sin(xy)z^{2})
tangent of y=(-4x)/(x^2+1),(0,0)	tangent\:y=\frac{-4x}{x^{2}+1},(0,0)
xy^'-4y=-2x	xy^{\prime\:}-4y=-2x
(\partial)/(\partial x)(xarccos(x))	\frac{\partial\:}{\partial\:x}(x\arccos(x))
integral of cos(x)*x	\int\:\cos(x)\cdot\:xdx
integral of (2)/(t^2)	\int\:\frac{2dt}{t^{2}}dx
inverse oflaplace (10)/(s^2+2*s+10)	inverselaplace\:\frac{10}{s^{2}+2\cdot\:s+10}
integral of (x^2)/(x^3-1)	\int\:\frac{x^{2}}{x^{3}-1}dx
derivative of ln(sqrt(x)+7)	\frac{d}{dx}(\ln(\sqrt{x}+7))
derivative of 3^{tan(x})	\frac{d}{dx}(3^{\tan(x)})
(dy)/(dx)=(y^2+2xy)/(x^2)	\frac{dy}{dx}=\frac{y^{2}+2xy}{x^{2}}
integral of (1-2x)/(x(1-x))	\int\:\frac{1-2x}{x(1-x)}dx
tangent of (-4x)/(x^2+1)	tangent\:\frac{-4x}{x^{2}+1}
derivative of (x-4^2)	\frac{d}{dx}((x-4)^{2})
integral of ((1-x)^3)/(x^3sqrt(x))	\int\:\frac{(1-x)^{3}}{x^{3}\sqrt{x}}dx
d/(dt)(e^{3t}cos(2t))	\frac{d}{dt}(e^{3t}\cos(2t))
derivative of f(x)=ln(4-x^8)	derivative\:f(x)=\ln(4-x^{8})
(d^2y)/(dx^2)-49(dy)/(dx)=e^{7x}	\frac{d^{2}y}{dx^{2}}-49\frac{dy}{dx}=e^{7x}
integral from 0 to 1 of xcos(2pix)	\int\:_{0}^{1}x\cos(2πx)dx
derivative of-2x+5	derivative\:-2x+5
integral of xsec^2(6x)	\int\:x\sec^{2}(6x)dx
integral of (6x^5-5/(x^5))	\int\:(6x^{5}-\frac{5}{x^{5}})dx
(dy)/(dx)=(e^x)/(9+e^x)	\frac{dy}{dx}=\frac{e^{x}}{9+e^{x}}
(1+x)y^'=(x+2)(y-1)	(1+x)y^{\prime\:}=(x+2)(y-1)
limit as x approaches x/6 of cot(x)	\lim\:_{x\to\:\frac{x}{6}}(\cot(x))
slope of y=x^2+5x	slope\:y=x^{2}+5x
area 16x, 4/x , 1/4 x	area\:16x,\frac{4}{x},\frac{1}{4}x
integral of (sin(x))/(sqrt(4-cos(x)))	\int\:\frac{\sin(x)}{\sqrt{4-\cos(x)}}dx
(\partial)/(\partial x)((z^2+2x+y)/(xy))	\frac{\partial\:}{\partial\:x}(\frac{z^{2}+2x+y}{xy})
limit as x approaches 3+of e^{2/(3-x)}	\lim\:_{x\to\:3+}(e^{\frac{2}{3-x}})
integral of x*cos(nx)	\int\:x\cdot\:\cos(nx)dx
integral of 4x-4x^2	\int\:4x-4x^{2}dx
derivative of 1+9/25 y^4	derivative\:1+\frac{9}{25}y^{4}
laplacetransform-5t	laplacetransform\:-5t
derivative of arcsin(3x^4)	\frac{d}{dx}(\arcsin(3x^{4}))
slope of (2,8),(4,6)	slope\:(2,8),(4,6)
(dy)/(dx)=(6y^3)/((3-2x)^2),y(0)=-1	\frac{dy}{dx}=\frac{6y^{3}}{(3-2x)^{2}},y(0)=-1
integral of (t^2)/2	\int\:\frac{t^{2}}{2}dt
limit as x approaches 0 of (ln(x))/x	\lim\:_{x\to\:0}(\frac{\ln(x)}{x})
integral of 1/((x^2-5)^{3/2)}	\int\:\frac{1}{(x^{2}-5)^{\frac{3}{2}}}dx
derivative of tan(2)(x+1)	derivative\:\tan(2)(x+1)
(dy)/(dx)-8y=5	\frac{dy}{dx}-8y=5
(\partial)/(\partial x)(1/(xcos(z)))	\frac{\partial\:}{\partial\:x}(\frac{1}{x\cos(z)})
integral of (3x)/(2e^{6x)}	\int\:\frac{3x}{2e^{6x}}dx
integral from 0 to 5 of 1/(x^{15/14)}	\int\:_{0}^{5}\frac{1}{x^{\frac{15}{14}}}dx
derivative of ln(x-4y)	\frac{d}{dx}(\ln(x-4y))
derivative of f(x)=(x^3+3)e^x	derivative\:f(x)=(x^{3}+3)e^{x}
derivative of 1/6 x^2-3x+15	derivative\:\frac{1}{6}x^{2}-3x+15
integral of cos(y)cos(4y)	\int\:\cos(y)\cos(4y)dy
area 2x-x^2,-3	area\:2x-x^{2},-3
derivative of 3tan(sqrt(x))	\frac{d}{dx}(3\tan(\sqrt{x}))
integral of 1/((1-x^4))	\int\:\frac{1}{(1-x^{4})}dx
derivative of sqrt(cos(xsin(x)))	\frac{d}{dx}(\sqrt{\cos(x)\sin(x)})
integral of tanh(2x)	\int\:\tanh(2x)dx
integral of 1/(2x+4x^2)	\int\:\frac{1}{2x+4x^{2}}dx
f(x)=(x^2)/(100)	f(x)=\frac{x^{2}}{100}
inverse oflaplace 3/((s+4)(s+8)^2)	inverselaplace\:\frac{3}{(s+4)(s+8)^{2}}
integral of (cos(5x))	\int\:(\cos(5x))dx
derivative of 2^{sqrt(ln(x)})	\frac{d}{dx}(2^{\sqrt{\ln(x)}})
derivative of y=cos(a^4+x^4)	derivative\:y=\cos(a^{4}+x^{4})
slope of (7,5),(-4,-1)	slope\:(7,5),(-4,-1)
integral from 0 to pi/4 of sec^5(x)	\int\:_{0}^{\frac{π}{4}}\sec^{5}(x)dx
derivative of f(x)=\sqrt[8]{x^3}-x^pi	derivative\:f(x)=\sqrt[8]{x^{3}}-x^{π}
integral of x/(sqrt(-5x^2+2x+1))	\int\:\frac{x}{\sqrt{-5x^{2}+2x+1}}dx
derivative of 8(x+4^{3/2})	\frac{d}{dx}(8(x+4)^{\frac{3}{2}})
limit as x approaches-2 of (x+1)/(1-x^2)	\lim\:_{x\to\:-2}(\frac{x+1}{1-x^{2}})
derivative of {r}(xcos(x))	\frac{d}{dx}({r}(x)\cos(x))
integral of y*cos(xy)	\int\:y\cdot\:\cos(xy)dx
sum from n=0 to infinity of 1	\sum\:_{n=0}^{\infty\:}1
limit as x approaches 1 of 2/((x-1)^2)	\lim\:_{x\to\:1}(\frac{2}{(x-1)^{2}})
integral of 1/(sqrt(x)-\sqrt[3]{x)}	\int\:\frac{1}{\sqrt{x}-\sqrt[3]{x}}dx
derivative of y=(18)/(x^2+2)	derivative\:y=\frac{18}{x^{2}+2}
y^'=e^{x-y},y(0)=2	y^{\prime\:}=e^{x-y},y(0)=2
integral of s7^s	\int\:s7^{s}ds
(\partial)/(\partial x)(ln(x+9y+4z))	\frac{\partial\:}{\partial\:x}(\ln(x+9y+4z))
limit as x approaches 2 of 5x-7	\lim\:_{x\to\:2}(5x-7)
integral of (x^4+1)/(x(x^2+2)^2)	\int\:\frac{x^{4}+1}{x(x^{2}+2)^{2}}dx
limit as x approaches pi of ln\|cos(x)-9\|	\lim\:_{x\to\:π}(\ln\left\|\cos(x)-9\right\|)
derivative of-sec(pi/3)+2sec^3(pi/3)	derivative\:-\sec(\frac{π}{3})+2\sec^{3}(\frac{π}{3})
integral of 20-0.01x	\int\:20-0.01xdx
derivative of 5e^x(cos(x)-sin(x))	derivative\:5e^{x}(\cos(x)-\sin(x))
derivative of sqrt(sin(x-1))	\frac{d}{dx}(\sqrt{\sin(x-1)})
integral from 0 to 2 of x^23^x	\int\:_{0}^{2}x^{2}3^{x}dx
derivative of (7cos(x-8)/(sin(x)))	\frac{d}{dx}(\frac{7\cos(x)-8}{\sin(x)})
integral of 3csc(x)cot(x)	\int\:3\csc(x)\cot(x)dx
integral of x/(x^4+10)	\int\:\frac{x}{x^{4}+10}dx
partialfraction x/(x-1)	partialfraction\:\frac{x}{x-1}
derivative of x(1-x^2)	\frac{d}{dx}(x(1-x)^{2})
simplify log_{10}((arcsin(x))^2)	simplify\:\log_{10}((\arcsin(x))^{2})
(-x^3+4x^2-5x)^'	(-x^{3}+4x^{2}-5x)^{\prime\:}
limit as (x,y) approaches (pi, pi/2) of ysin(x-y)	\lim\:_{(x,y)\to\:(π,\frac{π}{2})}(y\sin(x-y))
tangent of f(x)=(x^2-8)^5,\at x=3	tangent\:f(x)=(x^{2}-8)^{5},\at\:x=3

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