Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) §4.1 The Chain Rule, #55 · Calculus · Differentiation rules

If … and … then … and

If $f = x^{4}$ and $g = x^{3}$ then $f^{'} = 4 x^{3}$ and $g^{'} = 3 x^{2}$ . The chain rule multiplies derivatives to get $12 x^{5}$ . But $f (g (x)) = x^{12}$ and its derivative is not $12 x^{5}$ . Where is the flaw?

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Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) · §4.1 The Chain Rule, #55

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