Answer:
[tex]\displaystyle f'(0.3) = \arccos (0.3)[/tex]
General Formulas and Concepts:
Calculus
Differentiation
- Derivatives
- Derivative Notation
Integration
Integration Rule [Fundamental Theorem of Calculus 2]: [tex]\displaystyle \frac{d}{dx}[\int\limits^x_a {f(t)} \, dt] = f(x)[/tex]
Step-by-step explanation:
Step 1: Define
Identify
[tex]\displaystyle f(x) = \int\limits^x_0 {\arccos (t)} \, dt[/tex]
Step 2: Differentiate
- Integration Rule [Fundamental Theorem of Calculus 2]: [tex]\displaystyle f'(x) = \arccos (x)[/tex]
Step 3: Evaluate
- Substitute in x [Function]: [tex]\displaystyle f'(0.3) = \arccos (0.3)[/tex]
Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Integration
