Part 1/4:

Understanding the Quotient Rule in Calculus

Calculus is a branch of mathematics that focuses on rates of change and slopes of curves. Among its various rules, the Quotient Rule is essential for finding the derivative of a function composed of the division of two other functions. This article delves into the derivation of the Quotient Rule, provides a practical example, and highlights its applications.

The Quotient Rule Defined

When we have a function represented as:

[

y = \frac{f(x)}{g(x)},

]

the derivative of this function can be represented using the Quotient Rule, which states:

[

y' = \frac{g(x) \cdot f'(x) - f(x) \cdot g'(x)}{[g(x)]^2}.

]

Here, ( f'(x) ) and ( g'(x) ) are the derivatives of the functions ( f(x) ) and ( g(x) ), respectively.