How Do You Calculate the Partial Derivatives of f(x, y) = xy² + x²y?

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SUMMARY

The discussion centers on calculating the partial derivatives of the function f(x, y) = xy² + x²y. Participants clarify the notation, specifically distinguishing between Δƒ/Δx and ∂ƒ/∂x. The consensus is that both partial derivatives can be computed using fundamental calculus techniques. Assaf emphasizes that these calculations are straightforward and encourages sharing specific attempts to resolve any confusion.

PREREQUISITES
  • Understanding of partial derivatives in multivariable calculus
  • Familiarity with the function notation f(x, y)
  • Basic knowledge of calculus concepts such as differentiation
  • Ability to interpret mathematical notation, including Δ and ∂ symbols
NEXT STEPS
  • Review the rules for calculating partial derivatives of functions
  • Practice finding partial derivatives of similar functions, such as f(x, y) = x²y + y³
  • Explore the concept of difference quotients in calculus
  • Study the applications of partial derivatives in optimization problems
USEFUL FOR

Students studying calculus, educators teaching multivariable calculus, and anyone interested in understanding the fundamentals of partial derivatives.

tnacrew
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Δƒ/Δx and Δƒ/Δy. ƒ(x,y) = xy² + x²y

anyone able to calculate?
 
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I'm not sure what you mean by [tex]\frac{\Delta f}{\Delta x}[/tex]. Do you mean [tex]\frac{\partial f}{\partial x}[/tex]?

At any rate, why don't you tell us what you've tried and where you get stuck?

--------
Assaf
http://www.physicallyincorrect.com/"
 
Last edited by a moderator:
Whether you mean the partial derivatives or the "difference quotients" those are both pretty straightforward by methods you learned in elementary calculus. How have you tried to do them?
 

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