Implicit Differentiation Quiz

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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)?

  • Product rule
  • Power rule
  • Chain rule (correct)
  • Quotient rule

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)?

  • 0
  • 2x
  • \(dy/dx\) (correct)
  • 2y

When can implicit differentiation be useful?

<p>When solving equations for (y) explicitly (A)</p> Signup and view all the answers

What is the derivative of (y^2) with respect to (y)?

<p>(2y) (A)</p> Signup and view all the answers

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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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