Partial Derivatives - Multivariable Calculus | Summary and Q&A

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May 19, 2017
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The Organic Chemistry Tutor
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Partial Derivatives - Multivariable Calculus

TL;DR

Learn how to find partial derivatives of functions with respect to specific variables using the power rule and the product rule.

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Key Insights

  • 🫡 Partial derivatives involve finding the derivative of a function with respect to a specific variable while treating other variables as constants.
  • ✊ The power rule is used to find the derivative of a term that only involves the variable of interest.
  • 📏 The product rule is used to find the derivative of functions that involve multiple variables.

Transcript

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Questions & Answers

Q: How do you find the partial derivative of a function with respect to a certain variable?

To find the partial derivative, treat the variable of interest as the only variable and view all other variables as constants. Then, use the power rule or the product rule to differentiate the function.

Q: What is the power rule?

The power rule states that the derivative of x to the power of n is n times x to the power of n-1. This rule is used when finding the derivative of a term that only involves the variable of interest.

Q: When do you use the product rule?

The product rule is used when differentiating functions that involve multiple variables. It allows you to find the derivative of the product of two functions by differentiating each function separately and combining the results.

Q: How can you determine which variables are treated as constants and which are differentiated?

When finding the partial derivative with respect to a certain variable, all other variables should be treated as constants. Only the variable of interest should be differentiated.

Summary & Key Takeaways

  • Partial derivatives involve finding the derivative of a function with respect to one variable while treating the other variables as constants.

  • The power rule states that the derivative of x to the power of n is n times x to the power of n-1.

  • The product rule is used when differentiating functions that involve multiple variables.

  • It is important to correctly identify which variables are treated as constants and which are differentiated in the partial derivatives.

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