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THE CHAIN RULE If g is differentiable at x and f is differentiable at g(x), then the composite function F = fg defined by
THE CHAIN RULE If g is differentiable at x and f is differentiable at g(x), then the composite function F = fg defined by F(x) = f(g(x)) is differentiable at x and F' is given by the product F'(x) = f'(g(x)) g'(x) In Leibniz notation, if y = f (u) and u dy = dx g(x) are both differentiable functions, then dy du du dx Note: addition formula to execute next assignment d (ax) = a* In a dx 18. h(t) = (t 1)(t + 1)4 2 20. v = (x + 1) / x + 2
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