**Question:**

We have a function which takes a two-dimensional input $x = (x_1, x_2)$ and has two parameters $w = (w_1, w_2)$ given by $f(x, w) = σ(σ(x1w1)w_2 + x_2)$ where $σ(x) = 1/(1+e^{-x}))$ . We use backpropagation to estimate the right parameter values. We start by setting both the parameters to 0. Assume that we are given a training point x1 = 1, x2 = 0, y = 5. Given this information answer the next two questions. What is the value of $∂f/∂w_2$?

**Solution:**

Write $σ(x_1w_1)w_2 + x_2$ as $o_2$ and $x_1w_1$ as $o_1$ $∂f/∂w_2=∂f/∂o_2*∂o_2/∂w_2$

$∂f/∂w_2= σ(o_2)(1 − σ(o_2)) × σ(o_1)$ # Need to understand here

$∂f/∂w_2 = 0.5 ∗ 0.5 ∗ 0.5 =0.125$

Can some one help me to understand the solution? What is the $f$ equation, which partially derivated with $o_2$ to get $σ(o_2)(1 − σ(o_2))$?

And not understood, from where $0.5$ came.

Please help.