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- - **path dependent function with a definite path**
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path dependent function with a definite pathThis question is about if I have a path dependent function but a deinite path, then can I take partial derivatives? And are the points that are along path A connected to the points that are along path B. If I consider a non-conservative vector field I must specify a path, in this case the path is always: (eq. 1) and integrate along the path to create the field: (eq. 2) and also: (eq. 3) may I now treat t as path independent? In other words, may I now take the total derivative and evaluate at a constant x like this: (eq. 4) (eq. 5) and then evaluate eq. 5 at a fixed x so that dx = 0 It seems to me that I can't do this because I think that I have defined a relationship between dx and dz in equation 1. Since t is path dependent, p must be in the definition of t so setting dx = 0 violates the constraint that p has set on the relationship between dx and dz. Is what I was thinking correct? Or am I allowed to take the total derivative of X and set dx = 0? Is the point t(x,z) connected to t(x,z+dz)? I am posting this question here and in the differentials section because I am not sure if this is a question about disconnected space or conservative fields. |

Re: path dependent function with a definite pathI should have mentioned that all paths go through the origin and x and z can only be positive. |

Re: path dependent function with a definite pathQuote:
Is the vector field two dimentional or three dimentional ?? |

Re: path dependent function with a definite pathIt is 2 dimensional. |

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