vela said:Your answer is fine. Wolfram's answer is weird.
A derivative is a mathematical concept that represents the rate of change of a function at a specific point. It tells us how much the output of a function changes when the input changes.
We simplify derivatives to make them easier to work with and understand. Simplifying a derivative helps us identify patterns and relationships between different functions.
The basic rules for simplifying derivatives include the power rule, product rule, quotient rule, and chain rule. These rules help us find the derivative of more complex functions by breaking them down into simpler parts.
Simplifying a derivative can help us find the maximum and minimum values of a function, determine the slope of a curve, and solve optimization problems. It also allows us to analyze the behavior of a function and make predictions about its future values.
Yes, there are several shortcuts for simplifying derivatives, such as using tables of derivatives, memorizing common derivatives, or using software programs or calculators. However, it is important to understand the basic rules for simplifying derivatives to ensure accuracy and avoid mistakes.