Does the gradiant change when stretching coordinates?

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When stretching coordinates in a Cartesian system by a factor of 2, the gradient remains unchanged as it represents the rate of change of a function. This can be verified by substituting the stretched coordinates into a known problem and observing the differentiation process. The discussion also touches on the analogy of converting speed units, questioning if a car traveling at x m/s is equivalent to traveling at x mph, highlighting the importance of understanding unit conversions. Overall, the gradient's consistency under coordinate transformation emphasizes its fundamental nature in calculus. The relationship between gradients and coordinate transformations is crucial for accurate mathematical modeling.
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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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