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Find the derivative of the function.$ g(x) = e^{x^2 - x} $

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00:18

Frank Lin

Calculus 1 / AB

Chapter 3

Differentiation Rules

Section 4

The Chain Rule

Derivatives

Differentiation

Harvey Mudd College

Baylor University

University of Nottingham

Boston College

Lectures

04:40

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.

44:57

In mathematics, a differentiation rule is a rule for computing the derivative of a function in one variable. Many differentiation rules can be expressed as a product rule.

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Find the derivative of the…

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find the derivative of the…

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Let's find the derivative of G of X and G of X is a composite function. It has one function inside the other. The outside function is the E to the X function, and the inside function is the X squared minus X function. Now remember the derivative of each of the exes, each of the X, So the derivative of E to the something will be e to the something times the derivative of the inside. So are derivatives going to be the derivative of the outside E to the something so e to the X squared minus x times the derivative of the inside? So the derivative of that power to X minus one

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