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Problem

Differentiate the function. $ f(x) = 2^{40} $

00:19

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Problem 2 Easy Difficulty

(a) Sketch, by hand, the graph of the function $ f(x) = e^x, $ paying particular attention to the graph crosses the y-axes.
What fact allows you to do this?
(b) What types of functions are $ f(x) = e^x $ and $ g(x) = x^e? $
Compare the differentiation formulas for $ f $ and $ g. $
(c) Which of the two functions in part (b) grows more rapidly when $ x $ is large?


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01:31

Amy Jiang

Related Courses

Calculus 1 / AB

Calculus: Early Transcendentals

Chapter 3

Differentiation Rules

Section 1

Derivatives of Polynomials and Exponential Functions

Related Topics

Derivatives

Differentiation

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Top Calculus 1 / AB Educators
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Lectures

Video Thumbnail

04:40

Derivatives - Intro

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.

Video Thumbnail

44:57

Differentiation Rules - Overview

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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Watch More Solved Questions in Chapter 3

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Problem 7
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Problem 9
Problem 10
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Problem 12
Problem 13
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Problem 16
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Problem 18
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Problem 26
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Problem 38
Problem 39
Problem 40
Problem 41
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Problem 45
Problem 46
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Problem 48
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Problem 51
Problem 52
Problem 53
Problem 54
Problem 55
Problem 56
Problem 57
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Problem 59
Problem 60
Problem 61
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Problem 67
Problem 68
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Problem 81
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Problem 86

Video Transcript

and slower. So when you read here so we're gonna draw a graph for part A. We have X is equal to eat the axe, and when Xs equal to zero, we have a wide value of one. The derivative is equal to eat the axe, so on access equal to zero, the derivative is equal to one, so it's increasing when it cuts the Y axis. For part B, we have f of X is exponential and it's defined for all ex Brian's and it's equal to FX. G of X is equal to X to the e and it's defined for only positive values of X, the derivative of F ISS needs the axe, then the derivative of G this e times x to the A minus one for part c Well, you see that FX is equal to eat. The X grows more rapidly when x this large compared to Jesus the X because when you see the graph up of X looks like this g of x, well, look like this

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Calculus: Early Transcendentals

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Grace He

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Lectures

Video Thumbnail

04:40

Derivatives - Intro

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.

Video Thumbnail

44:57

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Join Course
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