Quotient Rule for Derivatives

The Quotient Rule says that the derivative of a quotient is the denominator times the derivative of the numerator minus the numerator times the derivative of the denominator, all divided by the square of the denominator,

Heron's formula

Heron's formula gives the area of a triangle when the lengths of all three sides are known. Given the lengths of the three sides of a triangle, a, b, c, the area of the triangle can be determined as

A = \sqrt{s(s-a)(s-b)(s-c)}

where s = \dfrac{a+b+c}{2} , semi-perimeter of the triangle.

The formula can be transformed to the following interesting forms.