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On another thread that I can't find I found a message from jamesrc about differentiating cos of sinx that says:

df(g(x))/dx = df(g)/dg * dg(x)/dx by the chain rule, this part I get and I thank james for the help the thing that confuses me is why df(g)/dg = cos(cosx).

Aren't we differentiating df(g) wrt (g) which would give -sin(sinx). What am I missing?