text: ## Friday, February 26, 2016
  
  Here's an example of solving for dy/dx using implicit differentiation
  
  y^2 + 2xy^3 - 3x^2 = 14
  
  2y(dy/dx) + 2x(3y^2)(dy/dx) + 2y^3 - 6x = 0
  
  2y(dy/dx) + 6xy^2(dy/dx) = 6x - 2y^3
  
  dy/dx(2y +6xy^2) = 6x - 2y^3
  
  dy/dx = (6x-2y^3)/(6xy^2 + 2y)
  
  dy/dx = (3x-y^3)/(3xy^2 + y)
explanation: The document provides an example of solving for \( \frac{dy}{dx} \) using implicit differentiation. It includes a step-by-step solution to the problem but does not contain a specific question or a question-and-answer format.
distilabel_metadata.content: Evaluate the user given text extract and determine if it contains a math question and optionally and answer to this question.
  
  Output rules:
  
  1. Briefly describe the document and mention if it contains a question or a question and answer.
  2. Finalize the output with: Label: no-question,question,question-and-answer,multiple-question,multiple-question-and-answer
distilabel_metadata.role: system
distilabel_metadata.content: ## Friday, February 26, 2016
  
  Here's an example of solving for dy/dx using implicit differentiation
  
  y^2 + 2xy^3 - 3x^2 = 14
  
  2y(dy/dx) + 2x(3y^2)(dy/dx) + 2y^3 - 6x = 0
  
  2y(dy/dx) + 6xy^2(dy/dx) = 6x - 2y^3
  
  dy/dx(2y +6xy^2) = 6x - 2y^3
  
  dy/dx = (6x-2y^3)/(6xy^2 + 2y)
  
  dy/dx = (3x-y^3)/(3xy^2 + y)
distilabel_metadata.role: user
distilabel_metadata.raw_output_q_a_detector_0: The document provides an example of solving for \( \frac{dy}{dx} \) using implicit differentiation. It includes a step-by-step solution to the problem but does not contain a specific question or a question-and-answer format.
  
  Label: no-question