A radio disc jockey has 8 songs on this upcoming hours playlist: 3 are rock songs,2 are reggae, and 3 are country songs. The dis
2 answers:
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Answer:
General Formulas and Concepts:
<u>Calculus</u>
Differentiation
- Derivatives
- Derivative Notation
Derivative Property [Multiplied Constant]:
Derivative Property [Addition/Subtraction]:
Derivative Rule [Basic Power Rule]:
- f(x) = cxⁿ
- f’(x) = c·nxⁿ⁻¹
Derivative Rule [Product Rule]:
Derivative Rule [Quotient Rule]:
Derivative Rule [Chain Rule]:
Step-by-step explanation:
*Note:
Since the answering box is <em>way</em> too small for this problem, there will be limited explanation.
<u>Step 1: Define</u>
<em>Identify.</em>
<u>Step 2: Differentiate</u>
We can differentiate this function with the use of the given <em>derivative rules and properties</em>.
Applying Product Rule:
Differentiating the first portion using Quotient Rule:
Apply Derivative Rules and Properties, namely the Chain Rule:
Differentiating the second portion using Quotient Rule again:
Apply Derivative Rules and Properties, namely the Chain Rule again:
Substitute in derivatives:
Simplify:
We can rewrite the differential by factoring and common mathematical properties to obtain our final answer:
∴ we have found our derivative.
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Learn more about derivatives: brainly.com/question/26836290
Learn more about calculus: brainly.com/question/23558817
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Topic: Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Differentiation
