Answer:
General Formulas and Concepts:
Pre-Algebra
Algebra II
- Natural logarithms ln and Euler's number e
- Logarithmic Property [Dividing]:
- Logarithmic Property [Exponential]:
Calculus
Differentiation
- Derivatives
- Derivative Notation
- Implicit Differentiation
Derivative Property [Multiplied Constant]:
Derivative Property [Addition/Subtraction]:
Basic Power Rule:
- f(x) = cxⁿ
- f’(x) = c·nxⁿ⁻¹
Derivative Rule [Quotient Rule]:
Derivative Rule [Chain Rule]:
Explanation:
Step 1: Define
Identify
Step 2: Rewrite
- [Equality Property] ln both sides:
- Expand [Logarithmic Property - Dividing]:
- Simplify [Logarithmic Property - Exponential]:
Step 3: Differentiate
- Implicit Differentiation:
- Logarithmic Differentiation [Derivative Rule - Chain Rule]:
- Basic Power Rule:
- Simplify:
- Isolate
:
- Substitute in y [Derivative]:
- Simplify:
- Simplify:
Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Differentiation
Book: College Calculus 10e