What is what does f'(x) mean?

f'(x) represents the derivative of the function f(x) with respect to the variable x. It's a fundamental concept in calculus and signifies the instantaneous rate of change of f(x) at a specific point x.

Here's a breakdown of what f'(x) means:

• Rate of Change: f'(x) gives you the rate at which the function f(x) is changing as x changes. Think of it as the slope of the tangent line to the graph of f(x) at the point x.
• Slope of Tangent Line: Geometrically, f'(x) is the slope of the line tangent to the curve of f(x) at the point (x, f(x)). You can learn more about tangent lines at https://www.wikiwhat.page/kavramlar/Tangent%20Line.
• Instantaneous Rate: The derivative provides the instantaneous rate of change. This is different from the average rate of change, which is calculated over an interval.
• Notation: f'(x) is just one way to denote the derivative. Other common notations include dy/dx (if y = f(x)), and Df(x). You can read about this from https://www.wikiwhat.page/kavramlar/Derivative%20Notation.
• Finding the Derivative: The process of finding f'(x) is called differentiation. This involves using various rules and techniques, such as the power rule, product rule, quotient rule, and chain rule. An extensive look at this can be found here https://www.wikiwhat.page/kavramlar/Differentiation%20Rules.
• Applications: Derivatives have widespread applications in various fields, including physics (velocity, acceleration), economics (marginal cost, marginal revenue), optimization problems (finding maximum and minimum values), and many more. It is very important to understand https://www.wikiwhat.page/kavramlar/Applications%20of%20Derivatives.