Implicit differentiation
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Whenever you're faced with a function with both x and y on one side of the equation, utilize implicit differentiation to take the derivative!
Scenario: Evaluate the derivative of the function below.
Notice... both x and y occur on the right-side of the equation! This means we must use implicit differentiation!
- Evaluate the derivative on both sides of the expression
- Find all terms that include the derivative of y (dy/dx)
- Isolate the derivative of y (dy/dx) terms on one side of the equation
Whenever taking the derivative of y in implicit differentiation, treat it as x. Then, multiply it by the derivative of y, a.k.a. (dy/dx)!
Answer: The derivative of y (a.k.a. (dy/dx) or y') equals (2x + 2y) / (1 - 2y - 2x).