Find the partial derivatives of the function

In summary, partial derivatives are derivatives that measure the rate of change of a function with respect to one of its variables while holding all other variables constant. To find them, you can use the limit definition of a derivative or the rules of differentiation. They are useful in analyzing the rate of change of a multivariable function and can be applied in many fields. The main difference between partial derivatives and total derivatives is that partial derivatives only consider the change in one variable while total derivatives consider the change in all variables. While most functions have well-defined partial derivatives, there are some cases where they may not exist or may be difficult to find.
  • #1
cwesto
18
0
The problem:
f(x,y)=-[tex]\frac{-7x-2y}{9x+7y}[/tex]

find:

fx(x,y)
fy(x,y)

The attempt:

fx(x,y)=[tex]\frac{-7-2y}{9+7y}[/tex]
fy(x,y)=[tex]\frac{-7x-2}{9x+7}[/tex]

Questions:

I'm not exactly sure how to find the partail derivative with a fraction like this one.
 
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  • #2
use the quotient rule for differentiation? or product rule but with (9+7y)^(-1) for eg.

is this homework? it looks like the wrong forum to me
 
  • #3
Oh sorry.
 

Related to Find the partial derivatives of the function

What is the definition of partial derivatives?

Partial derivatives are a type of derivative that measures the rate of change of a function with respect to one of its variables, while holding all other variables constant. It is denoted by ∂f/∂x, where f is the function and x is the variable of interest.

How do you find the partial derivatives of a function?

To find the partial derivatives of a function, you can use the limit definition of a derivative or the rules of differentiation. For the limit definition, you take the limit of the difference quotient as the change in the variable of interest approaches 0. For the rules of differentiation, you treat all other variables as constants and use the appropriate rule for the variable of interest.

Why do we use partial derivatives?

Partial derivatives are used to analyze the rate of change of a function with respect to a specific variable in a multivariable function. They can help us understand how a function changes as one variable changes while holding all other variables constant. This is useful in many fields, such as physics, economics, and engineering.

What is the difference between partial derivatives and total derivatives?

The main difference between partial derivatives and total derivatives is that partial derivatives only consider the change in one variable while holding all other variables constant, while total derivatives consider the change in all variables. In other words, partial derivatives are local changes, while total derivatives are global changes.

Can you find the partial derivatives of any function?

In most cases, yes, you can find the partial derivatives of any function. However, there are some functions that may not have well-defined partial derivatives, such as non-continuous functions or functions with discontinuous first-order derivatives. In these cases, the partial derivatives may not exist or may be difficult to find.

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