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let y = e^(2x), let u = 2x, so y = e^u

chain rule: du/dx * dy/du = 2*e^u = 2e^u = 2e^(2x)

this is the solution copied from my book, my question is why do they let u = 2x? is e^u the same as e^x? If so then wouldn't all derivatives of the exponential functions be in the form of f`(x)e^(f(x))??