text: # Consider The Following. W = Yz/X, X = Θ2, Y = R + 7θ, Z = R − 7θ (A) Find ∂W/∂R And ∂W/∂Θ By Using The Appropriate Chain
  
  Consider The Following. W = Yz/X, X = Θ2, Y = R + 7θ, Z = R − 7θ (A) Find ∂W/∂R And ∂W/∂Θ By Using The Appropriate Chain
  
  1) Consider the following.
  
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  w = yz/x, x = θ2y = r + 7θz = r − 7θ
  
  (a) Find ∂w/∂r and ∂w/∂θ by using the appropriate Chain Rule.
  
   ∂w ∂r
  =
   ∂w ∂θ
  =
  
  (b) Find ∂w/∂r and ∂w/∂θ by converting w to a function of r and θ before differentiating.
  
   ∂w ∂r
  =
   ∂w ∂θ
  =
  
  2) Evaluate fxfy and fz at the given point.
  
  f(xyz) = x2y3 + 7xyz − 5yz, (−1, 2, 1)
  
   fx(−1, 2, 1) =
   fy(−1, 2, 1) =
  
  3) For f(xy), find all values of x and y such that fx(xy) = 0 and fy(xy) = 0 simultaneously.
  
  f(xy) = x2 + 4xy + y2 − 18x − 12y + 14
  
  (xy) =
explanation: The document contains multiple math questions and no answers. The questions are related to partial derivatives and evaluating functions at specific points.
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: # Consider The Following. W = Yz/X, X = Θ2, Y = R + 7θ, Z = R − 7θ (A) Find ∂W/∂R And ∂W/∂Θ By Using The Appropriate Chain
  
  Consider The Following. W = Yz/X, X = Θ2, Y = R + 7θ, Z = R − 7θ (A) Find ∂W/∂R And ∂W/∂Θ By Using The Appropriate Chain
  
  1) Consider the following.
  
  Save Time On Research and Writing
  Hire a Pro to Write You a 100% Plagiarism-Free Paper.
  
  w = yz/x, x = θ2y = r + 7θz = r − 7θ
  
  (a) Find ∂w/∂r and ∂w/∂θ by using the appropriate Chain Rule.
  
   ∂w ∂r
  =
   ∂w ∂θ
  =
  
  (b) Find ∂w/∂r and ∂w/∂θ by converting w to a function of r and θ before differentiating.
  
   ∂w ∂r
  =
   ∂w ∂θ
  =
  
  2) Evaluate fxfy and fz at the given point.
  
  f(xyz) = x2y3 + 7xyz − 5yz, (−1, 2, 1)
  
   fx(−1, 2, 1) =
   fy(−1, 2, 1) =
  
  3) For f(xy), find all values of x and y such that fx(xy) = 0 and fy(xy) = 0 simultaneously.
  
  f(xy) = x2 + 4xy + y2 − 18x − 12y + 14
  
  (xy) =
distilabel_metadata.role: user
distilabel_metadata.raw_output_q_a_detector_0: The document contains multiple math questions and no answers. The questions are related to partial derivatives and evaluating functions at specific points.
  
  Label: multiple-question