Messy partial differentials with chain rule.

In summary, the conversation discusses finding the partial derivatives of z with respect to x and y at a given point (x=1, y=2) on a surface defined implicitly by an equation. The approach to solving this problem is not clear and help is requested.
  • #1
phewy13
2
0

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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  • #2

FAQ: Messy partial differentials with chain rule.

What is a partial differential?

A partial differential is a type of mathematical equation that involves multiple independent variables and their partial derivatives. It is commonly used in physics and engineering to describe how a system changes over time or in different conditions.

What is the chain rule in partial differentials?

The chain rule in partial differentials is a method for finding the partial derivatives of a function that depends on multiple variables. It states that the partial derivative of a function with respect to one variable can be found by taking the partial derivative of the function with respect to another variable and multiplying it by the partial derivative of that variable with respect to the original variable.

How is the chain rule applied in messy partial differentials?

In messy partial differentials, the chain rule is applied by first identifying the variables involved and their corresponding partial derivatives. These derivatives are then substituted into the chain rule formula and simplified to find the partial derivative of the function.

What makes partial differentials with chain rule messy?

Partial differentials with chain rule can become messy when there are multiple variables and complicated functions involved. It can be difficult to keep track of all the derivatives and properly apply the chain rule formula, leading to messy and complex equations.

How can I solve messy partial differentials with chain rule?

Solving messy partial differentials with chain rule requires practice and patience. It is important to carefully identify the variables and their derivatives, and to take your time when applying the chain rule formula. It may also be helpful to break down the equation into smaller, more manageable parts and then combine them to find the final solution.

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