Find the derivative: y={ (3x+1)cos(2x) } / e^2x
1 answer:
Answer:
General Formulas and Concepts:
<u>Pre-Algebra</u>
Order of Operations: BPEMDAS
- Brackets
- Parenthesis
- Exponents
- Multiplication
- Division
- Addition
- Subtraction
<u>Algebra I</u>
- Factoring
- Exponential Rule [Dividing]:
- Exponential Rule [Powering]:
<u>Calculus</u>
Derivatives
Derivative Notation
Derivative of a constant is 0
Basic Power Rule:
- f(x) = cxⁿ
- f’(x) = c·nxⁿ⁻¹
Product Rule:
Quotient Rule:
Trig Derivative:
eˣ Derivative:
Step-by-step explanation:
<u>Step 1: Define</u>
<u>Step 2: Differentiate</u>
- [Derivative] Quotient Rule:
- [Derivative] [Fraction - Numerator] eˣ derivative:
- [Derivative] [Fraction - Denominator] Exponential Rule - Powering:
- [Derivative] [Fraction - Numerator] Product Rule:
- [Derivative] [Fraction - Numerator] [Brackets] Basic Power Rule:
- [Derivative] [Fraction - Numerator] [Brackets] (Parenthesis) Simplify:
- [Derivative] [Fraction - Numerator] [Brackets] Trig derivative:
- [Derivative] [Fraction - Numerator] Factor:
- [Derivative] [Fraction] Simplify [Exponential Rule - Dividing]:
- [Derivative] [Fraction - Numerator] Factor:
Topic: AP Calculus AB/BC
Unit: Derivatives
Book: College Calculus 10e
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the height:
(with g being the gravitational acceleration)
Answer:
2: yes
Step-by-step explanation: