This notation is ambiguous, because it is not clear whether you differentiate ##f## w.r.t. the first or second variable. So I would writehojoon yang said:Hi
I understood above differential
## typo. RHS= 2*f ' (x,2z-x)
Same comment as above. Change the first ##f'## to ##D_1f## and the second ##f'## to ##D_2f##.hojoon yang said:but, what is answer of below equation?
is this right?
f ' ( g(z),2z-x) * g' (z) + f ' ( g(z),2z-x) *2
Multi variable differential is a mathematical concept that deals with the rates of change of multiple variables simultaneously. It involves calculating the partial derivatives of a function with respect to each of the variables.
Multi variable differential allows us to understand how a function changes in response to changes in multiple variables, which is crucial in many scientific fields such as physics, engineering, and economics. It also helps us to optimize functions and make predictions based on multiple variables.
The main difference is that single variable differential only involves calculating the derivative of a function with respect to one variable, while multi variable differential involves calculating the partial derivatives with respect to each of the variables.
Multi variable differential is used in many real-world applications, such as in modeling physical systems, optimizing processes in engineering, and predicting market trends in economics. It is also used in machine learning and data analysis to understand and predict complex relationships between multiple variables.
There are various techniques for solving multi variable differential equations, including the chain rule, implicit differentiation, and the method of separation of variables. Other methods such as gradient descent and Newton's method are also commonly used for optimization problems.