How do I solve this first order partial derivative problem?

In summary, The conversation discusses finding the first order derivative in a problem involving multiple variables and a combination of functions. The method involves treating one variable as a constant and differentiating with respect to the other. This can be done by replacing the constant variable with a specific value, like 17 or pi, and then finding the derivative normally.
  • #1
Spectre32
136
0
We went over this breifly in class and I'm confused on it. Were doing first order only and this is the problem: z = 3x^2*y^3*e^(5x-3y) + ln(2x^2 + 3y^3) I know your susposed to Fx(x,y) and treat X or Y as a constant, depending, upon how you want to start, but I'm still unclear as to how to solve this.

Thanks for the help.
 
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  • #2
Well you know how to find an ordinary derivative, so if you need to get Fx, replace y by something else, like a or 17 or pi or whatever, then find the x derivative.
 
  • #3
So you just single each variable out and that's it?
 
  • #4
You treat the variable you are not differentiating with respect to as any other constant, and then you differentiate normally.

Setting the variable equal to 17 or pi or something would probably confuse lots of people, though...

cookiemonster
 
  • #5
yeah i was confused by that.
 
  • #6
Spectre32 said:
So you just single each variable out and that's it?

yeah that's it. Fix one (pretend it's constant), differentiate with respect to the other.
 

1. What is a partial derivative?

A partial derivative is a mathematical concept used in multivariable calculus to calculate the rate of change of one variable with respect to another while holding all other variables constant. It is denoted by ∂ (partial symbol) and is often used in the study of functions with multiple independent variables.

2. How is a partial derivative calculated?

A partial derivative is calculated by taking the derivative of a function with respect to one variable while treating all other variables as constants. This is similar to taking a regular derivative, but instead of finding the slope of a curve at a single point, the partial derivative gives the rate of change in a specific direction.

3. What is the difference between a partial derivative and a total derivative?

A partial derivative calculates the rate of change of one variable with respect to another, while holding all other variables constant. A total derivative, on the other hand, calculates the overall rate of change of a function with respect to all of its variables. In other words, the total derivative takes into account the changes in all variables, while the partial derivative only considers changes in one variable.

4. What is the purpose of finding a partial derivative?

Partial derivatives are used in many fields of science and engineering, including physics, economics, and engineering. They are used to study and understand how changes in one variable affect another variable in a given system. This information can be used to optimize functions and make predictions about the behavior of complex systems.

5. Can a partial derivative be negative?

Yes, a partial derivative can be negative. This means that as the variable in question increases, the other variable in the function decreases. For example, if the partial derivative of a function is negative with respect to time, it means that as time increases, the function decreases. This information is useful in understanding the relationships between variables in a system.

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