THE CHAIN RULE

df[g(x)]/dx = limh --ɬ {f[g(x + h)] - f [g(x)]}/h =

limh --ɬ {f[g(x + h) - g(x) + g(x)] - f [g(x)]}/h =

limh --ɬ {f[(dg(x)/dx) h) + g(x)] - f [g(x)]}/h =

limh --ɬ {f[g(x) + dg(x)] - f [g(x)]}/h =

limh --ɬ {f[g(x ) + dg(x)] - f [g(x)]}/dg(x)}*dg(x)/h

df/dg * dg/dx

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