Question

See attached photo, calc ab, please show work too!

Answer 1

(B) 15

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

1. Brackets
2. Parenthesis
3. Exponents
4. Multiplication
5. Division
6. Addition
7. Subtraction

• Left to Right

Algebra I

• Functions
• Function Notation

Calculus

Derivatives

Derivative Notation

Derivative Rule [Chain Rule]:
`\displaystyle (d)/(dx)[f(g(x))] =f'(g(x)) \cdot g'(x)`

Explanation:

Step 1: Define

h(x) = f(g(x))

h'(1) = ?

Step 2: Differentiate

1. Chain Rule: h'(x) = f'(g(x)) · g'(x)

Step 3: Evaluate

1. Substitute in x [Derivative]: h'(1) = f'(g(1)) · g'(1)
2. [Values] Substitute in function values: h'(1) = f'(3) · -3
3. [Values] Substitute in derivative function values: h'(1) = -5 · -3
4. Multiply: h'(1) = 15

Topic: AP Calculus AB/BC (Calculus I/II)

Unit: Derivatives

Book: College Calculus 10e