\\
Feed \ forwarding \\
net_1=xw_{1}+b \\
h=\sigma (net_1) \\
net_2=hw_{2}+b \\
{y}'=\sigma (net_2) \\ \\

Loss \ function \\
L=\frac{1}{2}\sum(y-{y}')^{2} \\ \\

Gradient \ calculation \ (Refer \ mattmazur's \ and \ DattA's tutorial)\\ \\
\frac{\partial L}{\partial w_{2}}=\frac{\partial net_2}{\partial w_2}\frac{\partial {y}' }{\partial net_2}\frac{\partial L }{\partial {y}'} \\ \\

\frac{\partial L}{\partial w_{1}}= \frac{\partial net_1}{\partial w_{1}} \frac{\partial h}{\partial net_1}\frac{\partial net_2}{\partial h}\frac{\partial {y}' }{\partial net_2}\frac{\partial L }{\partial {y}'} \\ \\ \\

Where: \\ \\
\frac{\partial L }{\partial {y}'}=\frac{\partial (\frac{1}{2}\sum(y-{y}')^{2})}{\partial {y}'}=({y}'-y) \\ \\
\frac{\partial {y}' }{\partial net_2}={y}'(1-{y}')\\ \\
\frac{\partial net_2}{\partial w_2}= \frac{\partial(hw_{2}+b) }{\partial w_2}=h \\ \\
\frac{\partial net_2}{\partial h}=\frac{\partial (hw_{2}+b) }{\partial h}=w_2 \\
\frac{\partial h}{\partial net_1}=h(1-h) \\ \\
\frac{\partial net_1}{\partial w_{1}}= \frac{\partial(xw_{1}+b) }{\partial w_1}=x \\ \\

\\
The \ gradients \ can \ be \ rewritten \ as: \\ \\
\frac{\partial L }{\partial w_2 }=h\times {y}'(1-{y}')\times ({y}'-y) \\ \\
\frac{\partial L}{\partial w_{1}}=x\times h(1-h)\times  w_2 \times {y}'(1-{y}')\times ({y}'-y) \\ \\

Weight \ update \\
w_{i}^{t+1} \leftarrow w_{i}^{t}-\alpha \frac{\partial L}{\partial w_{i}}