Partial Differentiation with 2 variables

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SUMMARY

The discussion focuses on finding the partial derivatives dz/dx and dz/dy for the function z = f(xy). To solve this, one must apply the chain rule of differentiation, treating y as a constant when differentiating with respect to x, and vice versa for y. The correct approach involves recognizing that the function is dependent on the product of x and y, necessitating the use of the product rule in conjunction with the chain rule.

PREREQUISITES
  • Understanding of partial differentiation
  • Familiarity with the chain rule in calculus
  • Knowledge of the product rule in differentiation
  • Basic concepts of multivariable functions
NEXT STEPS
  • Study the application of the chain rule in multivariable calculus
  • Learn about the product rule for differentiation
  • Explore examples of partial differentiation with composite functions
  • Practice solving partial derivatives of functions involving multiple variables
USEFUL FOR

Students studying calculus, particularly those focusing on multivariable functions and partial differentiation techniques.

Lonely Lemon
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Homework Statement



When I write 'd' I mean the partial differentiation symbol 'del' here...

Find dz/dx and dz/dy of:

z=f(xy)

I'm guessing this isn't a case of simply pretending the 'f( )' isn't there, how do I approach this problem?

Homework Equations





The Attempt at a Solution

 
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when you say
dz/dx
you want to find the first partial derivative of z in terms of x.
meaning, that you treat y as a constant and x as a veritable

similarly goes with dz/dy
 

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