Table of contents
- 0. Functions7h 52m
- Introduction to Functions16m
- Piecewise Functions10m
- Properties of Functions9m
- Common Functions1h 8m
- Transformations5m
- Combining Functions27m
- Exponent rules32m
- Exponential Functions28m
- Logarithmic Functions24m
- Properties of Logarithms34m
- Exponential & Logarithmic Equations35m
- Introduction to Trigonometric Functions38m
- Graphs of Trigonometric Functions44m
- Trigonometric Identities47m
- Inverse Trigonometric Functions48m
- 1. Limits and Continuity2h 2m
- 2. Intro to Derivatives1h 33m
- 3. Techniques of Differentiation3h 18m
- 4. Applications of Derivatives2h 38m
- 5. Graphical Applications of Derivatives6h 2m
- 6. Derivatives of Inverse, Exponential, & Logarithmic Functions2h 37m
- 7. Antiderivatives & Indefinite Integrals1h 26m
2. Intro to Derivatives
Derivatives as Functions
Problem 3.7.25a
Textbook Question
Derivatives using tables Let and . Use the table to compute the following derivatives.
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a.
![](/channels/images/assetPage/verifiedSolution.png)
1
Step 1: Recognize that the function h(x) = f(g(x)) is a composition of functions, and to find its derivative h'(x), we need to use the chain rule.
Step 2: The chain rule states that if h(x) = f(g(x)), then h'(x) = f'(g(x)) * g'(x).
Step 3: To find h'(3), substitute x = 3 into the expression for h'(x), giving us h'(3) = f'(g(3)) * g'(3).
Step 4: Use the table to find the values of g(3), f'(g(3)), and g'(3). First, find g(3) from the table.
Step 5: Once you have g(3), use the table to find f'(g(3)) and g'(3), then multiply these values to find h'(3).
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