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If $ g(x) = x/e^x, $ find $ g^{(n)}(x). $

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03:01

Frank Lin

Calculus 1 / AB

Chapter 3

Differentiation Rules

Section 2

The Product and Quotient Rules

Derivatives

Differentiation

Missouri State University

Oregon State University

Baylor University

Idaho State University

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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it's clear. So when you read here so we're given G of X is equal to X over each. The X prefers gonna find the first derivative, and we're gonna make a pattern out of it. You get one times each the X minus B to the x times X overeat the X square, and we get this is equal to one minus X over each X for a second derivative. After we simplify and everything, you get negative two plus X over each the X and for their derivative, you get three minus ranks over E to the X. So here we see that the denominators are all equal to eat the x No for the numerator. They switch off from positive to negative to positive and the numerator constant is equal to end. So it becomes negative one to the end. Power times X minus and for the numerator. So we got G. The end becomes equal to negative one on times X minus and over each the x

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