Mixed Partial and non-partial derivative definition

AI Thread Summary
The discussion focuses on the interpretation of the gradient vector of a function f in relation to both partial and non-partial derivatives. It clarifies that the gradient is expressed as grad f(x,y,z) = [∂f/∂x, ∂f/∂y, ∂f/∂z], highlighting the role of partial derivatives in defining the gradient. The equation provided illustrates how to represent the gradient vector using unit vectors i, j, and k for each variable. Additionally, it suggests that if the interpretation is unclear, one should consider the application of the chain rule to partial derivatives. Understanding these concepts is essential for analyzing functions of multiple variables.
terryphi
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Hi,

I have a derivative that states

grad f(x,y,z) = [die f/dx ; die f/dy; die f/dz]

I'm just wondering how I should interpret this partial derivative with respect to a non partial derivative.
 
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If you're looking to find the gradient vector to some function f of parameters x. y, z.. Try the following equation:

\nabla f = \frac{\partial f}{\partial x}i + \frac{\partial f}{\partial y}j + \frac{\partial f}{\partial z}k

Where the i j k components are the partial derivatives of the function f with respect to the indicated variable.

If this is not what you're referring to you may need to look at the chain rule as it applies to partial derivatives.
 
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