교과서 질문
The following limits represent f'(a) for some function f and some real number a.
b. Evaluate the limit by computing f'(a).
lim x🠂1 x¹⁰⁰-1 / x-1
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Ch. 3 - Derivatives
Briggs3rd EditionCalculus: Early TranscendentalsISBN: 9780136847243
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TOC.tableOfContents
- Ch. 1 - Functions210
- Ch. 2 - Limits371
- Ch. 3 - Derivatives633
- Ch. 4 - Applications of the Derivative412
- Ch. 5 - Integration328
- Ch. 6 - Applications of Integration331
- Ch. 7 - Logarithmic, Exponential Functions, and Hyperbolic Functions177
- Ch. 8 - Integration Techniques394
- Ch. 9 - Differential Equations179
- Ch. 10 - Sequences and Infinite Series339
- Ch. 11 - Power Series218
- Ch.12 - Parametric and Polar Curves215
3장, 문제 84d
Use the given graphs of f and g to find each derivative. <IMAGE>
d/dx (f(f(x))) |x=4
검증된 단계별 안내1
Step 1: Understand the problem requires finding the derivative of a composite function, specifically f(f(x)), at x = 4.
Step 2: Apply the chain rule for derivatives, which states that the derivative of a composite function f(g(x)) is f'(g(x)) * g'(x).
Step 3: Identify the inner function g(x) as f(x) and the outer function f(g(x)) as f(f(x)).
Step 4: Evaluate the derivative of the outer function f'(f(x)) and the derivative of the inner function f'(x) at x = 4 using the given graphs.
Step 5: Multiply the derivatives from Step 4 according to the chain rule: f'(f(4)) * f'(4).
비슷한 문제에 대한 검증된 영상 답변:
이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.
영상 길이:
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주요 개념
질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.
Chain Rule
The Chain Rule is a fundamental principle in calculus used to differentiate composite functions. It states that if you have a function f(g(x)), the derivative is f'(g(x)) * g'(x). This rule is essential for finding the derivative of functions where one function is nested inside another, as in the case of f(f(x)).
추천 영상:
05:02
Intro to the Chain Rule
Derivative
A derivative represents the rate of change of a function with respect to its variable. It is a measure of how a function's output value changes as its input value changes. Understanding how to compute derivatives is crucial for analyzing the behavior of functions, including finding slopes of tangent lines and optimizing functions.
추천 영상:
가이드 코스
05:44Derivatives
Evaluating Functions
Evaluating functions involves substituting specific values into a function to determine its output. In this context, after finding the derivative of f(f(x)), you will need to evaluate it at x=4. This step is important for obtaining a numerical result that reflects the behavior of the composite function at that particular point.
추천 영상:
가이드 코스
4:26Evaluating Composed Functions
관련 실천
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