In the example above, when multiplying x and y to obtain v, the engine will extend the graph to calculate the partial derivatives of the multiplication by using the multiplication derivative definition that it already knows.  and  . The resulting extended graph is shown in Figure 2, where the MultDerivative node also calculates the product of the resulting gradients by an input gradient to apply the chain rule; this will be explicitly seen in the following operations. Note that the backward graph (green nodes) will not be executed until all the forward steps are completed.