This slide shows that we can determine derivatives knowing just the rightmost df/df and the outputs in red.
eosofsky
To explain the math used to get the blue numbers,
df/df = 1,
df/da = z = 5,
df/dy = (df/da)(da/dy) = (z)(1) = z = 5,
df/dx = (df/da)(da/dx) = (z)(1) = z = 5,
df/dz = a = x + y = 3 + 4 = 7
This slide shows that we can determine derivatives knowing just the rightmost df/df and the outputs in red.
To explain the math used to get the blue numbers, df/df = 1, df/da = z = 5, df/dy = (df/da)(da/dy) = (z)(1) = z = 5, df/dx = (df/da)(da/dx) = (z)(1) = z = 5, df/dz = a = x + y = 3 + 4 = 7