[Jcrew]

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I understand how to find gradient (partial derivative x, y, z) but I have no clue what it means. Similarly, I read that rate of change in 3 dimensions just means the partial derivative, but I don't understand how to apply these two things.

Test Thursday, need help.

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It just means what is the rate of change of a function f(x,y,z) if you hold all but one of the variables constant.

Try to think of just the two variable case f(x,y). The partial derivative with respect to x of the function f describes how fast f changes if y is held constant along different values of x...or in other words just the contribution of the x variable to the f function's rate of change.