With these definitions we obtain the following partial derivatives
$$ \frac{\partial a}{\partial x} = 2x, $$and
$$ \frac{\partial b}{\partial a} = \exp{a}, $$and
$$ \frac{\partial c}{\partial a} = 1, $$and
$$ \frac{\partial c}{\partial b} = 1, $$and
$$ \frac{\partial d}{\partial c} = \frac{1}{2\sqrt{c}}, $$and finally
$$ \frac{\partial f}{\partial d} = 1. $$