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Sagot :
Answer:
[tex]\displaystyle f'(-3) = \frac{7}{9}[/tex]
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
- Brackets
- Parenthesis
- Exponents
- Multiplication
- Division
- Addition
- Subtraction
- Left to Right
Calculus
Derivatives
Derivative Notation
Derivative of a constant is a 0
Basic Power Rule:
- f(x) = cxⁿ
- f’(x) = c·nxⁿ⁻¹
Derivative Rule [Quotient Rule]: [tex]\displaystyle \frac{d}{dx} [\frac{f(x)}{g(x)} ]=\frac{g(x)f'(x)-g'(x)f(x)}{g^2(x)}[/tex]
Step-by-step explanation:
Step 1: Define
[tex]\displaystyle f(x) = \frac{-7}{x}[/tex]
[tex]\displaystyle x = -3[/tex]
Step 2: Differentiate
- Quotient Rule: [tex]\displaystyle f'(x) = \frac{\frac{d}{dx}[7]x - \frac{d}{dx}[x](-7)}{x^2}[/tex]
- Basic Power Rule: [tex]\displaystyle f'(x) = \frac{(0)x - x^{1 - 1}(-7)}{x^2}[/tex]
- Simplify: [tex]\displaystyle f'(x) = \frac{(0)x - x^0(-7)}{x^2}[/tex]
- Simplify: [tex]\displaystyle f'(x) = \frac{(0)x - 1(-7)}{x^2}[/tex]
- Multiply: [tex]\displaystyle f'(x) = \frac{0 + 7}{x^2}[/tex]
- Add: [tex]\displaystyle f'(x) = \frac{7}{x^2}[/tex]
Step 3: Solve
- Substitute in x [Derivative]: [tex]\displaystyle f'(-3) = \frac{7}{(-3)^2}[/tex]
- Evaluate exponents: [tex]\displaystyle f'(-3) = \frac{7}{9}[/tex]
Topic: AP Calculus AB/BC (Calculus I/II)
Unit: Derivatives
Book: College Calculus 10e
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