Differentiate two variables functions

In summary, differentiating a two variable function involves finding the rate of change of the function with respect to one variable while holding the other constant. This is different from differentiating a single variable function where we only consider one variable. The purpose of differentiating a two variable function is to understand its behavior and solve optimization problems. Common techniques used for differentiation include the power rule, product rule, quotient rule, and chain rule. A two variable function can have multiple partial derivatives, each with respect to a different variable.
  • #1
chimay
81
7
Hi,
I am dealing with an equality of the form:
[tex]f(x)=g(y,z)[/tex]
and I need to compute ##dx##.
Is the following relation correct?
[tex]dx={(\frac{\partial f}{\partial x})}^{-1}( \frac{\partial g}{\partial y}dy + \frac{\partial g}{\partial z}dz )[/tex]

Thank you in advance.
 
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  • #2
Yes, that's correct. Of course it breaks down at points where ##\frac{\partial f}{\partial x}## is zero, but maybe that's not in the domain of interest.
 
  • #3
Thank you!
 

Related to Differentiate two variables functions

1. What does it mean to differentiate a two variable function?

When we differentiate a two variable function, we are finding the rate of change of the function with respect to one of its variables while holding the other variable constant. This is also known as finding the partial derivative of the function.

2. How is differentiating a two variable function different from differentiating a single variable function?

Differentiating a two variable function involves finding the rate of change with respect to one variable while holding the other constant, whereas differentiating a single variable function involves finding the rate of change with respect to that one variable.

3. What is the purpose of differentiating a two variable function?

Differentiating a two variable function allows us to understand the behavior of the function in terms of its individual variables. It also helps in optimization problems where we need to find the maximum or minimum value of the function.

4. What are some common techniques used to differentiate two variable functions?

Some common techniques used to differentiate two variable functions include the power rule, product rule, quotient rule, and chain rule. These techniques allow us to find the partial derivatives of functions that involve multiple variables.

5. Can a two variable function have more than one partial derivative?

Yes, a two variable function can have multiple partial derivatives, each with respect to a different variable. This is because the rate of change of the function can vary depending on which variable is being held constant.

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