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Find the derivative of the function using the definition of derivative. State the domain of the function and the domain of its derivative.

$ f(x) = x^2 - 2x^3 $

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Calculus 1 / AB

Chapter 2

Limits and Derivatives

Section 8

The Derivative as a Function

Limits

Derivatives

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Lectures

04:40

In mathematics, the limit of a function is the value that the function gets very close to as the input approaches some value. Thus, it is referred to as the function value or output value.

In mathematics, a derivative is a measure of how a function changes as its input changes. Loosely speaking, a derivative can be thought of as how much one quantity is changing in response to changes in some other quantity; for example, the derivative of the position of a moving object with respect to time is the object's velocity. The concept of a derivative developed as a way to measure the steepness of a curve; the concept was ultimately generalized and now "derivative" is often used to refer to the relationship between two variables, independent and dependent, and to various related notions, such as the differential.

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Find the derivative of the…

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