You are right- your logic is pseudo math!lelandsthename said:
The difficulty is that g'(x) is NOT (f'(x))2. As Avodyne said, you need to use the chain rule: g(x)= u2 and u= f(x). dg/dx= (dg/du)(du/dx).A differentiable function is a mathematical function that is smooth and continuous, meaning that it has no abrupt changes or breaks. It is a function that can be represented by a smooth curve and has a well-defined derivative at every point.
Differentiability and continuity are closely related concepts. A function is differentiable at a point if it is continuous at that point and has a well-defined derivative. In other words, a function must be continuous in order to be differentiable.
Differentiable functions play a crucial role in calculus as they allow us to find the slope or rate of change of a function at any given point. This is important in many real-world applications, such as optimization problems and physics equations.
A function is differentiable if it is continuous and has a well-defined derivative at every point within its domain. This can be determined by checking for any discontinuities or sharp turns in the graph of the function.
There are several rules for differentiating a function, including the power rule, product rule, quotient rule, and chain rule. These rules allow us to find the derivative of more complex functions by breaking them down into smaller, simpler parts.