Implicit differentiation solving a function

In summary, the conversation is about solving the function xe^y and whether the x term should be eliminated to get the y term in the form of dy/dx. The solution involves using the product rule and possibly the chain rule.
  • #1
Jason03
161
0
Im trying to solve this function, that is part of a larger equation:

[tex]

\frac{d}{dx} xe^y

[/tex]

do I need to get rid of the x term so the y term is dy/dx?
 
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  • #2
Jason03 said:
Im trying to solve this function, that is part of a larger equation:

[tex]

\frac{d}{dx} xe^y

[/tex]

do I need to get rid of the x term so the y term is dy/dx?
I'm guessing that your attempting to evaluate the derivative, rather than 'solve' the function. I'm also assuming that y is a function of x, in which case you have a product of two functions of x. Hence, I would say that the product rule (followed by the chain rule) would be useful.
 
  • #3
thanks...I got it with the product rule!
 

1. What is implicit differentiation?

Implicit differentiation is a method used to find the derivative of a function where the dependent variable is not explicitly expressed in terms of the independent variable. This is common in equations that cannot be easily solved for the dependent variable.

2. How does implicit differentiation work?

Implicit differentiation involves treating the dependent variable as a function of the independent variable and using the chain rule to find its derivative. This means taking the derivative of each term in the equation and using the chain rule to differentiate any functions within the equation.

3. When should implicit differentiation be used?

Implicit differentiation is typically used when it is difficult or impossible to solve for the dependent variable in terms of the independent variable. It is also used when the equation involves both the dependent and independent variables and cannot be easily separated.

4. What are the steps for solving a function using implicit differentiation?

The steps for solving a function using implicit differentiation are as follows: 1) Take the derivative of each term in the equation, treating the dependent variable as a function of the independent variable. 2) Use the chain rule to differentiate any functions within the equation. 3) Simplify the resulting equation and solve for the derivative of the dependent variable.

5. Can implicit differentiation be used for any type of function?

Yes, implicit differentiation can be used for any type of function where the dependent variable is not explicitly expressed in terms of the independent variable. It is a versatile method that can be applied to a wide range of equations and functions.

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