Solve first order partial derivatives

In summary, use the chain rule to find the 1st order partial derivatives of g(s,t)=f(s,u(s,t),v(s,t)) where u(s,t)=st & v(s,t)=s+t, expressed in terms of s & t only. The partial derivatives can be calculated by taking the derivative of the function with respect to each variable while holding the other variables constant.
  • #1
jimjames
9
0

Homework Statement


Use the Chain Rule to find the 1. order partial derivatives of g(s,t)=f(s,u(s,t),v(s,t)) where u(s,t) = st & v(s,t)=s+t
The answer should be expressed in terms of s & t only.

I find the partial derivatives difficult enough and now there is no numbers in the problem, which confused me even more. Hopefully someone here can help me with how to solve this.

Homework Equations


g(s,t)=f(s,u(s,t),v(s,t)) where u(s,t) = st & v(s,t)=s+t

The Attempt at a Solution


(I have no idea what to do with this problem)
 
Physics news on Phys.org
  • #2
jimjames said:
(I have no idea what to do with this problem)

Partial derivatives are defined as derivatives of a function of multiple variables when all but the variable of interest are held fixed during the differentiation.
so calculate the partial derivatives with respect to s, and u and v whwere the partial derivative with respect to s will be taken when u.v are lept constant and in turn for the other two.
 

1. What is a first order partial derivative?

A first order partial derivative is a mathematical concept used in calculus to measure the rate of change of a multivariable function with respect to one of its variables. It represents the slope of the tangent line to the curve of the function in a specific direction.

2. How do you solve a first order partial derivative?

To solve a first order partial derivative, you need to first identify the variable with respect to which the derivative needs to be calculated. Then, you can use the rules of differentiation to find the derivative of the function with respect to that variable. This involves taking the derivative of each term in the function and combining them using the appropriate operations.

3. What is the purpose of solving first order partial derivatives?

The purpose of solving first order partial derivatives is to understand how a multivariable function changes with respect to one of its variables. This can be useful in various fields such as physics, engineering, and economics, where understanding the rate of change of a function is crucial.

4. Can you give an example of solving a first order partial derivative?

Sure, let's say we have the function f(x,y) = 3x^2 + 2xy + y^2. To find the partial derivative of f with respect to x, we first take the derivative of each term: fx = 6x + 2y. Therefore, the first order partial derivative of f with respect to x is 6x + 2y.

5. What are some common applications of first order partial derivatives?

First order partial derivatives have various applications in fields such as physics, engineering, economics, and statistics. They can be used to optimize functions, determine rates of change, and model real-world systems. For example, in physics, first order partial derivatives are used to calculate the velocity and acceleration of an object in motion.

Similar threads

Multivariable calculus proof involving the partial derivatives of an expression
    • Calculus and Beyond Homework Help
Replies
4
Views
643
Help explaining the chain rule please
    • Calculus and Beyond Homework Help
Replies
12
Views
2K
Lienard-Wiechert Potential derivation, chain rule
    • Calculus and Beyond Homework Help
Replies
1
Views
582
"Trick" for a specific potential function defined with an integral
    • Calculus and Beyond Homework Help
Replies
10
Views
2K
Finding the partial derivative from the given information
    • Calculus and Beyond Homework Help
Replies
2
Views
963
Differential Integration Problem
    • Calculus and Beyond Homework Help
Replies
4
Views
1K
Linear first-order differential equation with an initial condition
    • Calculus and Beyond Homework Help
Replies
5
Views
900
Understanding the Chain Rule in Multivariable Calculus
    • Calculus and Beyond Homework Help
Replies
15
Views
1K
I can't find my mistake in using the chain rule here
    • Calculus and Beyond Homework Help
Replies
17
Views
976
Solving Second Order Partial Derivative By Changing Variable
    • Calculus and Beyond Homework Help
Replies
5
Views
2K

Hot Threads

Recent Insights

Back
Top