In the above example we have introduced the variables a and b , and our function is
f(x) = f(a(x)) = b= \exp{a},with a=x^2 . We can decompose the derivative of f with respect to x as
\frac{df}{dx}=\frac{df}{db}\frac{db}{da}\frac{da}{dx}.We note that since b=f(x) that
\frac{df}{db}=1,leading to
\frac{df}{dx}=\frac{db}{da}\frac{da}{dx}=2x\exp{x^2},as before.