MeMoses said:Homework Statement
I have vector R. I need to show the R dot dR/dt = 0 => 1/2 d/dt[R dot R]
Homework Equations
The Attempt at a Solution
I guess I've never really applied the chain rule to dot products and its throwing me off. How does one go from R.dR/dt=0 to 1/2 d/dt[R.R] = 0. I have no idea to be honest. I'm not sure which direction to take it, all I know is it uses the chain rule. Sorry I haven't done much with this. I hope you can help. Thanks
The chain rule is a mathematical rule that allows us to calculate the derivative of a composite function. In other words, if a function is made up of multiple smaller functions, the chain rule tells us how to find the derivative of the overall function.
The chain rule is important because it allows us to solve more complex problems by breaking them down into smaller, simpler parts. This is useful in many areas of science, including physics, engineering, and economics.
To apply the chain rule, you first need to identify the inner and outer functions of the composite function. Then, you can use the formula: (outer function derivative) x (inner function derivative). This will give you the derivative of the overall function.
The dot product is a mathematical operation that takes two vectors and produces a scalar value. It is calculated by multiplying the corresponding elements of the two vectors and then adding them together.
The dot product is related to the chain rule because it is used to calculate the derivative of a vector-valued function. This is done by taking the dot product of the vector function with the gradient of the function, which is a vector that contains the partial derivatives of the function with respect to each of its variables.