Messy partial differentials with chain rule.

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SUMMARY

The discussion focuses on finding the partial derivatives \(\frac{\partial f}{\partial x}\) and \(\frac{\partial f}{\partial y}\) at the point (1, 2) for the implicit function defined by the equation \(2x^2y/z + 3z/xy - xy\sqrt{z} = 3\). The user initially equates \(\frac{\partial f}{\partial x}\) to \(\frac{\partial z}{\partial x}\) and attempts to compute the derivatives, resulting in a complex expression. The need for clarity and guidance in applying the chain rule for implicit differentiation is evident.

PREREQUISITES
  • Understanding of implicit differentiation
  • Familiarity with partial derivatives
  • Knowledge of the chain rule in calculus
  • Basic algebraic manipulation skills
NEXT STEPS
  • Review implicit differentiation techniques in calculus
  • Study the application of the chain rule for multivariable functions
  • Practice finding partial derivatives of implicit functions
  • Explore examples involving complex implicit equations
USEFUL FOR

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

phewy13
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Homework Statement


the problem asks: Find [tex]\delta[/tex]f/[tex]\delta/[/tex]x and [tex]\delta[/tex]f/[tex]\delta[/tex]y at x=1 and y=2 if z=f(x,y) is defined implicitly by 2x[tex]^{}2[/tex]y/z + 3z/xy - xy[tex]\sqrt{}z[/tex] = 3. Note that (1,2,4) is a point on the surface.


Homework Equations


Im not really sure how to approach this one.


The Attempt at a Solution



i started off by saying that [tex]\delta[/tex]f/[tex]\delta/[/tex]x is equal to [tex]\delta/[/tex]z/[tex]\delta/[/tex]x and i went through and found the partial derivatives of the above equation and it turned out really messy, any help would be greatly appreciated.
 
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