- #1
MatinSAR
- 520
- 174
- Homework Statement
- Find partial derivatives
- Relevant Equations
- dy/dx=(dy/dt)(dt/dx)
Can someone please help me to find out what happened here ?
That "tx" confused me ...ergospherical said:It's differentiating ##f## with respect to its arguments, then differentiating the arguments with respect to ##t##. It might be clearer if you write ##u = tx## and ##v=ty##, then
$$\partial f(u,v) / \partial t = (\partial f/ \partial u) (\partial u/ \partial t) + (\partial f/ \partial v) (\partial v/ \partial t)$$
Partial derivatives are a mathematical tool used to calculate the rate of change of a function with respect to one of its variables, while holding all other variables constant. They are important in science because they allow us to analyze how changes in one variable affect the overall behavior of a system or process.
To calculate a partial derivative, you first need to identify the variable you want to differentiate with respect to. Then, you treat all other variables as constants and use the standard rules of differentiation to find the derivative of the function with respect to the chosen variable.
The main difference between partial derivatives and ordinary derivatives is that partial derivatives consider changes in only one variable, while ordinary derivatives consider changes in all variables. In other words, partial derivatives measure the slope of a function in one direction, while ordinary derivatives measure the slope in all directions.
Partial derivatives are used in a wide range of real-world applications, including physics, engineering, economics, and statistics. They can be used to analyze the behavior of complex systems, optimize processes, and make predictions about future outcomes.
Some common mistakes when working with partial derivatives include forgetting to treat other variables as constants, using the wrong rules of differentiation, and not simplifying the final expression. It is important to carefully follow the steps and double-check your work to avoid these common errors.