Does the gradiant change when stretching coordinates?

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The discussion centers on the effect of stretching coordinates in a Cartesian coordinate system on the gradient of a function. It concludes that the gradient remains unchanged when coordinates are stretched by a factor of 2, as the gradient represents the rate of change of a function. Participants suggest testing this by substituting 2x for x in a known problem to observe the consistency of the gradient through differentiation.

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Homework Statement



Well, if you have given a gradiant in cartisian coordinate system? what happened to the gradiant if we stretched the coordinates by factor of 2?

Homework Equations

The Attempt at a Solution


I think gradiant should be the same as it's the rate of change of some function.
 
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You could test this yourself by taking a known problem where you have the gradient and subbing in 2x for x and see how it flows through the differentiations to get the gradient.
 
physicsfreak88 said:

Homework Statement



Well, if you have given a gradiant in cartisian coordinate system? what happened to the gradiant if we stretched the coordinates by factor of 2?

Homework Equations

The Attempt at a Solution


I think gradiant should be the same as it's the rate of change of some function.

If a car is traveling at x m/s, is it traveling at x mph?
 

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