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The derivative identity d/(dx)[f(x)g(x)] = lim_(h->0)(f(x+h)g(x+h)-f(x)g(x))/h (1) = (2) = lim_(h->0)[f(x+h)(g(x+h)-g(x))/h+g(x)(f(x+h)-f(x))/h] (3) = f(x)g^'(x)+g(x)f^'(x), ...

The formula giving the roots of a quadratic equation ax^2+bx+c=0 (1) as x=(-b+/-sqrt(b^2-4ac))/(2a). (2) An alternate form is given by x=(2c)/(-b+/-sqrt(b^2-4ac)). (3)

A skew coordinate system is a system of curvilinear coordinates in which each family of surfaces intersects the others at angles other than right angles. Skew coordinate ...

A number of attractive 24-compounds of the regular tetrahedron can be constructed. The compound illustrated above will be implemented in a future version of the Wolfram ...

The lines joining the vertices of a tetrahedron to the centroids of the opposite faces are called medians. Commandino's theorem states that the four medians of a tetrahedron ...

A totative is a positive integer less than or equal to a number n which is also relatively prime to n, where 1 is counted as being relatively prime to all numbers. The number ...

The tractrix spiral is a spiral with parametric equations x(t) = acostcos(t-tant) (1) y(t) = acostsin(t-tant) (2) for t in [0,pi/2). It is also known as the polar tractrix or ...

The integral transform obtained by defining omega=-tan(1/2delta), (1) and writing H(omega)=R(omega)+iX(omega), (2) where R(omega) and X(omega) are a Hilbert transform pair as ...

A t-(v,k,lambda) block design (abbreviated t-design) is an incidence structure of points and blocks such that the following hold: 1. There are v points, 2. Each block ...

cos(pi/(10)) = 1/4sqrt(10+2sqrt(5)) (1) cos((3pi)/(10)) = 1/4sqrt(10-2sqrt(5)) (2) cot(pi/(10)) = sqrt(5+2sqrt(5)) (3) cot((3pi)/(10)) = sqrt(5-2sqrt(5)) (4) csc(pi/(10)) = ...