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Popular Calculus Problems

derivative of (-x^2-4/((x^2-4)^2))	\frac{d}{dx}(\frac{-x^{2}-4}{(x^{2}-4)^{2}})
slope of (x^2+4)y=8	slope\:(x^{2}+4)y=8
integral from 0.5 to 1.5 of (1/8+3/8 x)	\int\:_{0.5}^{1.5}(\frac{1}{8}+\frac{3}{8}x)dx
integral of (3csc^2(4x))	\int\:(3\csc^{2}(4x))dx
d/(dv)(v/(u-v))	\frac{d}{dv}(\frac{v}{u-v})
16y^{''}-y=0	16y^{\prime\:\prime\:}-y=0
derivative of 5xsqrt(2)	\frac{d}{dx}(5x\sqrt{2})
integral from 1 to 2 of 16\sqrt[3]{2x-3}	\int\:_{1}^{2}16\sqrt[3]{2x-3}dx
(\partial)/(\partial x)(xsin(v))	\frac{\partial\:}{\partial\:x}(x\sin(v))
derivative of cosh^2(x-sinh^2(x))	\frac{d}{dx}(\cosh^{2}(x)-\sinh^{2}(x))
derivative of f(x)=x^5-x^3+3	derivative\:f(x)=x^{5}-x^{3}+3
integral from-27 to 1 of 1/(\sqrt[3]{x)}	\int\:_{-27}^{1}\frac{1}{\sqrt[3]{x}}dx
derivative of (2x+1)ln(x)	derivative\:(2x+1)\ln(x)
2ydx+e^{-3x}dy=0	2ydx+e^{-3x}dy=0
integral of (x^2+x-5)/(x^2-1)	\int\:\frac{x^{2}+x-5}{x^{2}-1}dx
integral of 5/(8x(x+1)^2)	\int\:\frac{5}{8x(x+1)^{2}}dx
integral of-e^{-2y}+1	\int\:-e^{-2y}+1dy
tangent of y= x/(x-5),(-1,a)	tangent\:y=\frac{x}{x-5},(-1,a)
integral from 6 to 8 of (48)/((x-6)^3)	\int\:_{6}^{8}\frac{48}{(x-6)^{3}}dx
(\partial)/(\partial x)(x/(y+8z))	\frac{\partial\:}{\partial\:x}(\frac{x}{y+8z})
integral from 1 to infinity of 6e^{-3x}	\int\:_{1}^{\infty\:}6e^{-3x}dx
derivative of u^{1/2}	derivative\:u^{\frac{1}{2}}
integral from 0 to 4 of 3e^{-2x}	\int\:_{0}^{4}3e^{-2x}dx
(\partial)/(\partial x)(x^1x^2+10x^1)	\frac{\partial\:}{\partial\:x}(x^{1}x^{2}+10x^{1})
y^3-(18x+8)+3xy^2((dy)/(dx))=0	y^{3}-(18x+8)+3xy^{2}(\frac{dy}{dx})=0
limit as x approaches 1 of sqrt(6)	\lim\:_{x\to\:1}(\sqrt{6})
integral of 1/x-1/(x^2)	\int\:\frac{1}{x}-\frac{1}{x^{2}}dx
xy^'=y+9x^2sin(x),y(pi)=0	xy^{\prime\:}=y+9x^{2}\sin(x),y(π)=0
(\partial)/(\partial z)(x/y+y/z)	\frac{\partial\:}{\partial\:z}(\frac{x}{y}+\frac{y}{z})
integral of 1/(kx-nx^2)	\int\:\frac{1}{kx-nx^{2}}dx
slope of (1.4)(-5)	slope\:(1.4)(-5)
integral of 6(sin(2x))/(sin(x))	\int\:6\frac{\sin(2x)}{\sin(x)}dx
integral of 1+3x+18x^2	\int\:1+3x+18x^{2}dx
limit as x approaches 0+of (ln(x)+1)/x	\lim\:_{x\to\:0+}(\frac{\ln(x)+1}{x})
inverse oflaplace (3(s+1))/(s^2+1/2)	inverselaplace\:\frac{3(s+1)}{s^{2}+\frac{1}{2}}
taylor e^{-x/2},0	taylor\:e^{-\frac{x}{2}},0
sum from n=2 to infinity of (1/2)^{3n}	\sum\:_{n=2}^{\infty\:}(\frac{1}{2})^{3n}
integral of 1/((-u^2+u-1))	\int\:\frac{1}{(-u^{2}+u-1)}du
derivative of e^{cos(x}+cos(e^x))	\frac{d}{dx}(e^{\cos(x)}+\cos(e^{x}))
derivative of (1+cos^2(x))^3	derivative\:(1+\cos^{2}(x))^{3}
(1+x^2)(dy)/(dx)=2xy+1	(1+x^{2})\frac{dy}{dx}=2xy+1
derivative of 2x^2sqrt(2-x)	\frac{d}{dx}(2x^{2}\sqrt{2-x})
derivative of (16/(x^2))	\frac{d}{dx}(\frac{16}{x^{2}})
(\partial)/(\partial y)(xy^3+x^2)	\frac{\partial\:}{\partial\:y}(xy^{3}+x^{2})
integral of (2+cos(x))/x	\int\:\frac{2+\cos(x)}{x}dx
d/(dj)(6i+8j)	\frac{d}{dj}(6i+8j)
(\partial)/(\partial y)(8xsin(y-z))	\frac{\partial\:}{\partial\:y}(8x\sin(y-z))
integral of sqrt(9x+1)	\int\:\sqrt{9x+1}dx
limit as x approaches 2 of 4/x	\lim\:_{x\to\:2}(\frac{4}{x})
integral from-3 to 3 of (\|x\|+10)	\int\:_{-3}^{3}(\left\|x\right\|+10)dx
integral of 3(x-3)(x+1)	\int\:3(x-3)(x+1)dx
inverse oflaplace-3	inverselaplace\:-3
area x=y^2-8y,x=3y-y^2	area\:x=y^{2}-8y,x=3y-y^{2}
integral of 10x+6	\int\:10x+6dx
y^{''}-(3/x)y^'-(4/(x^2))y=0	y^{\prime\:\prime\:}-(\frac{3}{x})y^{\prime\:}-(\frac{4}{x^{2}})y=0
integral of (((x+1)(x-1))/x)	\int\:(\frac{(x+1)(x-1)}{x})dx
integral of 22sin^2(x)cos^2(x)	\int\:22\sin^{2}(x)\cos^{2}(x)dx
integral from 0 to pi of sin(θ)	\int\:_{0}^{π}\sin(θ)dθ
integral of (e^x+sqrt(x))	\int\:(e^{x}+\sqrt{x})dx
derivative of 3^{4x+5}	\frac{d}{dx}(3^{4x+5})
integral of (3x^3+4x)e^{x^2}	\int\:(3x^{3}+4x)e^{x^{2}}dx
derivative of 1/10 x-1/4	\frac{d}{dx}(\frac{1}{10}x-\frac{1}{4})
integral of 3e^{x^2}	\int\:3e^{x^{2}}dx
derivative of 2-2cos^2(x)	derivative\:2-2\cos^{2}(x)
(\partial)/(\partial x)((x+3)^2)	\frac{\partial\:}{\partial\:x}((x+3)^{2})
sum from n=0 to infinity of sin(n)	\sum\:_{n=0}^{\infty\:}\sin(n)
derivative of sqrt(3+2x)	derivative\:\sqrt{3+2x}
derivative of (x^3+3)e^x	derivative\:(x^{3}+3)e^{x}
sum from n=1 to infinity of 1/((n(n+3)))	\sum\:_{n=1}^{\infty\:}\frac{1}{(n(n+3))}
integral of 1-2x	\int\:1-2xdx
derivative of a^2+2a+2	derivative\:a^{2}+2a+2
derivative of sech(2x)	\frac{d}{dx}(\sech(2x))
(\partial)/(\partial x)((3x+2y)^5)	\frac{\partial\:}{\partial\:x}((3x+2y)^{5})
limit as x approaches 4 of 1/(x-4)	\lim\:_{x\to\:4}(\frac{1}{x-4})
(dy)/(dx)=2x-3y	\frac{dy}{dx}=2x-3y
derivative of 4e^x+3xe^x	derivative\:4e^{x}+3xe^{x}
derivative of 4(x+2)^{3/2}	derivative\:4(x+2)^{\frac{3}{2}}
derivative of (sin(x+cos(x))sec(x))	\frac{d}{dx}((\sin(x)+\cos(x))\sec(x))
tangent of f(x)=sqrt(5x+4),\at x=1	tangent\:f(x)=\sqrt{5x+4},\at\:x=1
derivative of arctan(x+arccos(x))	\frac{d}{dx}(\arctan(x)+\arccos(x))
limit as x approaches infinity of 4x+5	\lim\:_{x\to\:\infty\:}(4x+5)
tangent of f(x)= 2/x ,\at x=2	tangent\:f(x)=\frac{2}{x},\at\:x=2
sum from n=1 to infinity of (2/n)^n*n!	\sum\:_{n=1}^{\infty\:}(\frac{2}{n})^{n}\cdot\:n!
(\partial)/(\partial x)(e^{sqrt(x)}ln(y))	\frac{\partial\:}{\partial\:x}(e^{\sqrt{x}}\ln(y))
limit as x approaches-3 of (3x)/(x+3)	\lim\:_{x\to\:-3}(\frac{3x}{x+3})
integral from 0 to 6x^2 of (t/(t+36))	\int\:_{0}^{6x^{2}}(\frac{t}{t+36})dt
derivative of 20-x	\frac{d}{dx}(20-x)
integral of x^{6/7}	\int\:x^{\frac{6}{7}}dx
derivative of 5x(sin(x)+cos(x))	derivative\:5x(\sin(x)+\cos(x))
d/(dθ)(2sin(2θ))	\frac{d}{dθ}(2\sin(2θ))
tangent of f(x)=6+5x^2-2x^3,\at x=1	tangent\:f(x)=6+5x^{2}-2x^{3},\at\:x=1
derivative of x^2+2xy	\frac{d}{dx}(x^{2}+2xy)
sum from n=0 to infinity of (e/(4pi))^n	\sum\:_{n=0}^{\infty\:}(\frac{e}{4π})^{n}
integral of (x^2+5x+4)/(x^2-2x+1)	\int\:\frac{x^{2}+5x+4}{x^{2}-2x+1}dx
derivative of tan(sec(cos(x)))	\frac{d}{dx}(\tan(\sec(\cos(x))))
slope of y^4-4y^2=x^4-9x^2,(-3,2)	slope\:y^{4}-4y^{2}=x^{4}-9x^{2},(-3,2)
derivative of (1/(y^2)-3/(y^4))(y+5y^3)	derivative\:(\frac{1}{y^{2}}-\frac{3}{y^{4}})(y+5y^{3})
(dy)/(dx)=(e^{x-y})	\frac{dy}{dx}=(e^{x-y})
integral from 2 to x^3 of t^4	\int\:_{2}^{x^{3}}t^{4}dt
y^{''}-2y^'-3y=3e^2t	y^{\prime\:\prime\:}-2y^{\prime\:}-3y=3e^{2}t

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