In calculus, the Quotient Rule is a formula that provides a method for finding the derivative of a function that is the ratio of two other functions. The rule is essential for calculus students and has important applications in many areas of science and engineering.
The quotient rule states that the derivative of a function that is the ratio of two other functions can be found by subtracting the product of the derivative of the numerator and the denominator from the product of the numerator and the derivative of the denominator, and then dividing the result by the square of the denominator. In other words, if f(x) = g(x)/h(x), then f'(x) = [g'(x)h(x) - g(x)h'(x)] / [h(x)]².
The quotient rule is essential for calculus students because it provides a method for finding the derivative of functions that are not easily differentiated using other methods. It is also useful in physics, engineering, and other fields that rely on calculus to solve complex problems.
The quotient rule was first developed by the mathematician Gottfried Wilhelm Leibniz in the 17th century, and it has since become an essential tool for mathematicians, scientists, and engineers in a wide range of disciplines.
In conclusion, the quotient rule is a formula that provides a method for finding the derivative of a function that is the ratio of two other functions. The rule is essential for calculus students and has important applications in many areas of science and engineering. The rule was first developed by the mathematician Gottfried Wilhelm Leibniz in the 17th century, and it remains an essential tool for mathematicians, scientists, and engineers in a wide range of disciplines today.
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