5 Questions
Which rule is used to find the derivative of (y^2) in the equation (x^2 + y^2 = 25)?
Chain rule
What is the derivative of (x^2) with respect to (x)?
2x
What is the derivative of (y) with respect to (x) in the equation (x^2 + y^2 = 25)?
(dy/dx)
When can implicit differentiation be useful?
When solving equations for (y) explicitly
What is the derivative of (y^2) with respect to (y)?
(2y)
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).
Test your understanding of implicit differentiation with this quiz! Learn how to find derivatives when (y) and (x) are mixed up in equations, and practice solving for (dy/dx) in various examples. Challenge yourself and master this important concept in calculus!
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