Partial diffrentiation HELP

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In summary, the conversation revolves around two problems related to partial differentiation. The first problem involves showing that Urr is equal to a combination of different variables. The second problem involves showing that a given equation satisfies the required conditions. However, more information and work is needed before any further help can be provided.
  • #1
theaviator
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Partial diffrentiation...URGENT PLZ HELP

Here are the two problems...

1- If U=(X,Y) X=F(R,S) Y=G(R,S)

SHOW THAT: Urr=(Wxx) (Fr)^2 + 2(Wxy) (Fr) (Gr)^2 + (Wx) (Frr) + (Wy)+ (Grr)


2- SHOW THAT: U(R,K)=R^n Cos(nk) satisfies the equation
Urr+1/r U + 1/(r^2) Ukk=0


that's urgent please help now if u can...thanks
 
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  • #2
You need to show some work before we can help you. Also, what is W in the first question? You have not defined it! For the second one, you simply take the required derivatives of U and plug then in.
 
  • #3
Use the chain rule- twice.
 

FAQ: Partial diffrentiation HELP

1. What is partial differentiation?

Partial differentiation is a mathematical concept used in multivariable calculus to calculate the rate of change of a function with respect to one of its variables while holding the other variables constant. It is used to analyze and solve problems involving functions with multiple variables.

2. Why is partial differentiation useful?

Partial differentiation allows us to understand how a function changes in response to changes in its independent variables. This is useful in many fields, such as physics, economics, and engineering, where variables are often interdependent and their relationships need to be studied.

3. How is partial differentiation different from ordinary differentiation?

Ordinary differentiation involves finding the rate of change of a function with respect to a single variable. Partial differentiation, on the other hand, deals with functions of multiple variables and calculates the rate of change with respect to one variable while treating the other variables as constants.

4. What are the basic rules for performing partial differentiation?

The basic rules for performing partial differentiation include treating all variables except the one being differentiated as constants, using the power rule for exponents, and applying the chain rule for functions of a single variable. Additionally, the product rule and quotient rule can also be applied when necessary.

5. How is partial differentiation used in real-world applications?

Partial differentiation is used in various real-world applications, such as optimizing production processes, analyzing stock market trends, and predicting weather patterns. It is also used in fields like physics, chemistry, and biology to model complex systems and understand their behavior.

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