Different between Partial and Ordinary derivative

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SUMMARY

The discussion clarifies the distinction between partial derivatives and ordinary derivatives in calculus. An ordinary derivative refers to the differentiation of a function with respect to a single variable, while a partial derivative involves differentiating a function with multiple variables concerning one specific variable. The conversation emphasizes the need to compare total derivatives of multivariable functions with their corresponding partial derivatives to provide a more comprehensive understanding of the topic.

PREREQUISITES
  • Understanding of basic calculus concepts
  • Familiarity with functions of multiple variables
  • Knowledge of differentiation techniques
  • Experience with ordinary and partial derivatives
NEXT STEPS
  • Research the concept of total derivatives in multivariable calculus
  • Study the applications of partial derivatives in physics and engineering
  • Explore the chain rule for functions of multiple variables
  • Learn about the geometric interpretation of partial derivatives
USEFUL FOR

Students studying calculus, particularly those in engineering or physics courses, as well as educators looking to deepen their understanding of derivatives in multivariable contexts.

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I took already Calculus and Ordinary differential equations but my fluids mechanics Professor ask us to write to pages about the difference between a partial and a ordinary derivative. The problem is that the only thing I know is that ordinary derivative are the differentiation of a function of one variable, and partial derivative the differentiation of a function of multiple variables about one variable.

This won't fill 2 pages. Somebody could help with some other differences?
 
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Comparing the total (ordinary) derivative of a function with multiple variables to the partial der. with resp. to one of the variables would be more illuminating and voluminous.
 

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