Question

5 Draw a computational graph to compute the function f(, y) ( graph to compute f (2,3) -y). Use the Draw a reverse mode graph to compute the derivatives f/0x and อ//ay for f 3( y). Use the graph to find those derivatives at 2 and 3. 6

Answer 1

5

Consider the equation

To draw the computational graph, we simplify the equation into it's constituent terms i.e.,

Let

$\Rightarrow f(x,y) = vu$

So,

f(2.3) =-8

For the reverse-mode graph, first we compute the partial derivatives :

23(4) 12

$\frac{\partial u}{\partial x} = \frac{\partial x}{\partial x} - \frac{\partial y}{\partial x} = 1$

$\frac{\partial u}{\partial y} = \frac{\partial x}{\partial y} - \frac{\partial y}{\partial y} = -1$

İJu Ou

8

$\frac{\partial f}{\partial x} = \frac{\partial f}{\partial v}\times \frac{\partial v}{\partial x} + \frac{\partial f}{\partial u}\times \frac{\partial u}{\partial x} = -12+8 = -4$

$\frac{\partial f}{\partial y} = \frac{\partial f}{\partial u}\times \frac{\partial u}{\partial y} = 8\times -1 = -8$

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