Math Problem Statement
Use the Quotient Rule to differentiate the function. f(t) = cos(t)/t^5
Solution
To differentiate the function using the Quotient Rule, recall the rule:
Here, and . Now, differentiate and :
Now, apply the Quotient Rule:
Simplify the numerator and denominator:
Factor the numerator:
Finally, simplify:
So, the derivative is:
Would you like further clarification or details on any step? Here are 5 related questions:
- What are the steps for applying the Product Rule in a similar function?
- How does the Power Rule apply to the differentiation of ?
- What is the significance of factoring in the numerator when using the Quotient Rule?
- Can you differentiate using a similar process?
- How would the derivative change if the function were ?
Tip: Always simplify expressions as much as possible after applying differentiation rules to make them easier to interpret.
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Math Problem Analysis
Mathematical Concepts
Calculus
Differentiation
Quotient Rule
Formulas
Quotient Rule: (d/dt)[u(t)/v(t)] = (v(t) * u'(t) - u(t) * v'(t)) / [v(t)]^2
Theorems
Quotient Rule
Suitable Grade Level
Grades 11-12