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 77b
Textbook Question
For x < 0, what is f′(x)?
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1
Step 1: Identify the function f(x) for which you need to find the derivative f'(x). Without the explicit form of f(x), we cannot proceed with differentiation.
Step 2: Once you have the function f(x), apply the rules of differentiation. Common rules include the power rule, product rule, quotient rule, and chain rule.
Step 3: If f(x) is a polynomial, use the power rule: for any term ax^n, the derivative is anx^(n-1).
Step 4: If f(x) involves trigonometric, exponential, or logarithmic functions, use the respective differentiation rules for these functions.
Step 5: After applying the appropriate rules, simplify the expression to find f'(x) for x < 0.
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