Webcurrently taking Measure and Integration course, which seems to have a different definition of f'. traditionally, f ′ ( x) = lim h → 0 f ( x + h) − f ( x) h but in folland's book, it seems to be defined as f ′ ( x) = lim r → 0 f ( x + r) − f ( x − r) m ( B ( x, r)) WebDec 16, 2014 · Start by defining the function a(x) = g(h(x)) The the chain rule gives us: (f ∘ g ∘ h)′(x) = (f ∘ α)′(x) = f ′(α(x))α′(x) Applying the definition of α(x) to the equation above gives us: f ′(α(x))α′(x) = f ′(g(h(x)))(g ∘ h)′(x) Using the chain rule again: f ′(g(h(x)))(g ∘ h)′(x) = f ′(g(h(x)))g′(h(x))h′(x) Therefore:
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