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Problem

If $ g(x) + x \sin g(x) = x^2, $ find $ g'(0). $
01:34

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Problem 21 Easy Difficulty

If $ f(x) + x^2[f(x)]^3 = 10 $ and $ f(1) = 2, $ find $ f'(1). $

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Related Courses

Calculus 1 / AB
Calculus: Early Transcendentals

Chapter 3

Differentiation Rules

Section 5

Implicit Differentiation

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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Recommended Videos

01:40

If $ f(x) + x^2[f(x)]^3 = …

01:00

Find $f(1)+f(2)+\cdots+f(1…

01:13

If $ f(2) = 10 $ and $ f&#…

01:52

$$
\text { If } f(x)=1+…

02:10

Find $f^{\prime \prime}(x)…

01:03

If $f(x)=\left\lfloor x-1 …

01:26

If $f(x)=|x-1|+\left\lflo…

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If $f(x)=x^{3}+x^{2}-x-1,$…

01:12

If $f(x)=x^{2}-2 x,$ find …

Watch More Solved Questions in Chapter 3

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Problem 6
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Problem 8
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Problem 10
Problem 11
Problem 12
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Problem 15
Problem 16
Problem 17
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Problem 20
Problem 21
Problem 21
Problem 22
Problem 23
Problem 24
Problem 25
Problem 26
Problem 27
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Problem 30
Problem 31
Problem 32
Problem 33
Problem 34
Problem 35
Problem 36
Problem 37
Problem 38
Problem 39
Problem 40
Problem 41
Problem 42
Problem 43
Problem 44
Problem 45
Problem 46
Problem 47
Problem 48
Problem 49
Problem 50
Problem 51
Problem 52
Problem 53
Problem 54
Problem 55
Problem 56
Problem 57
Problem 58
Problem 59
Problem 60
Problem 61
Problem 62
Problem 63
Problem 64
Problem 65
Problem 66
Problem 67
Problem 68
Problem 69
Problem 70
Problem 71
Problem 72
Problem 73
Problem 74
Problem 75
Problem 76
Problem 77
Problem 78
Problem 79
Problem 80

Video Transcript

So if you have this and give you eff off one Finance prime one. So here we take the derivative on both sides. The second term we use the product rule and Cheryl Sorry, this should be. Plus, it was a product. Russo thiss plus the first part times at the review of the second Power is chair or three f o x square of pry affects Ryan. Sighs of constants are details that the ring with him she gives you zero and you clubbing one. So you have private fun plus two times f Cuba's foreign killed eight plus three extra problem one. So disappear. My mommy is one. So you have the right and how and the FX is so if one is to so if one squares for half price for the hose hero. So you have one plus twelve this certain so certainly have pry off one horse. Negative sixteen. So that should keeps us f proffer one ecos negative sixteen over thirty

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Calculus: Early Transcendentals

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Related Topics

Derivatives

Differentiation
Top Calculus 1 / AB Educators
Kayleah Tsai

Harvey Mudd College

Caleb Elmore

Baylor University

Kristen Karbon

University of Michigan - Ann Arbor

Joseph Lentino

Boston College

Calculus 1 / AB Courses

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.
Join Course
Recommended Videos

01:40

If $ f(x) + x^2[f(x)]^3 = 10 $ and $ f(1) = 2, $ find $ f'(1). $

01:00

Find $f(1)+f(2)+\cdots+f(10)$ if $f(x)=2^{x}$.

01:13

If $ f(2) = 10 $ and $ f'(x) = x^2 f(x) $ for all x, find $ f''(2). $

01:52

$$ \text { If } f(x)=1+x+x^{2}+x^{3}+x^{4}+\cdots, \text { find } f\left(\frac…

02:10

Find $f^{\prime \prime}(x)$. $$f(x)=\left(2 x^{2}-3 x+1\right)^{10}$$

01:03

If $f(x)=\left\lfloor x-1 \mid+\left\lfloor x-3 \mid\right.\right.$, find $f^{\…

01:26

If $f(x)=|x-1|+\left\lfloor x-3 \mid\right.$, find $f^{\prime}(2)$

01:46

If $f(x)=x^{3}+x^{2}-x-1,$ find $f(1), f(-1), f\left(\frac{1}{2}\right),$ and $…

01:12

If $f(x)=x^{2}-2 x,$ find $f(a+1)$ and $f(a+2).$

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