Proving Formula in Vector Differentiation

In summary, the problem at hand is to prove the formula d (A∙B) = A∙dB + dA∙B and the individual is seeking an identity in vector differentiation to show that ΔA∙ΔB = 0. They are also inquiring about the limits involved in the general formula of vector differentiation.
  • #1
ppoorrttee
2
0
1. The problem statement
The formula that must be proven is:
d (A∙B) = A∙dB + dA∙B
du du du


2. The attempt at a solution
When I substitute the left side of the equation to the general formula of vector differentiation, I got the left side of the equation + ΔA∙ΔB
du
Now my only problem is that how can I prove that ΔA∙ΔB = 0 so that it will result to the above equation? Is there any identity in vector differentiation that is ΔA∙ΔB = 0?
 
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  • #2
First, what are [itex]\Delta A[/itex] and [itex]\Delta B[/itex]? The "general formula of vector differentiation" that I know involves limits. What limits are you taking?
 

1. What is vector differentiation?

Vector differentiation is a mathematical operation used to find the rate of change of a vector function. It involves taking the derivative of each component of the vector separately.

2. Why is proving formula in vector differentiation important?

Proving formula in vector differentiation is important because it allows us to use vector calculus to solve more complex problems in physics, engineering, and other fields. It also helps us to better understand the relationships between vectors and their derivatives.

3. What are some common formulas used in vector differentiation?

Some common formulas used in vector differentiation include the product rule, chain rule, and quotient rule. The gradient, divergence, and curl operators are also frequently used in vector differentiation.

4. How do you prove a formula in vector differentiation?

To prove a formula in vector differentiation, you must use the definition of the derivative and apply it to each component of the vector function. Then, simplify the resulting expression and compare it to the given formula to show that they are equivalent.

5. Are there any limitations to using vector differentiation?

Like any mathematical tool, vector differentiation has its limitations. It is not always applicable to all types of vector functions and may not be the most efficient method for solving certain problems. It also requires a solid understanding of vector algebra and calculus to use effectively.

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