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What is the difference between a Derivative and a Gradient?

What does f ' (x) mean?

Welcome to Merspi and thanks for the question! I've reformatted your question so that it's slightly easier to read.

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A derivative f'(x) is the "gradient function" of the original function f(x)

The derivative is not a gradient, but it will tell you the gradient of the original graph for any x you input. Hence it is a gradient function.