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Questions and Answers
Which rule is used to find the derivative of (y^2) in the equation (x^2 + y^2 = 25)?
Which rule is used to find the derivative of (y^2) in the equation (x^2 + y^2 = 25)?
- Product rule
- Power rule
- Chain rule (correct)
- Quotient rule
What is the derivative of (x^2) with respect to (x)?
What is the derivative of (x^2) with respect to (x)?
- 2x (correct)
- 0
- 2
- \(x^2\)
What is the derivative of (y) with respect to (x) in the equation (x^2 + y^2 = 25)?
What is the derivative of (y) with respect to (x) in the equation (x^2 + y^2 = 25)?
- 0
- 2x
- \(dy/dx\) (correct)
- 2y
When can implicit differentiation be useful?
When can implicit differentiation be useful?
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What is the derivative of (y^2) with respect to (y)?
What is the derivative of (y^2) with respect to (y)?
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Study Notes
Implicit Differentiation
- The rule used to find the derivative of (y^2) in the equation (x^2 + y^2 = 25) is implicit differentiation.
Derivatives
- The derivative of (x^2) with respect to (x) is (2x).
- The derivative of (y^2) with respect to (y) is (2y).
Implicit Differentiation in Context
- In the equation (x^2 + y^2 = 25), the derivative of (y) with respect to (x) can be found using implicit differentiation.
When to Use Implicit Differentiation
- Implicit differentiation can be useful when working with equations that cannot be explicitly solved for (y) in terms of (x).
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