Suppose $f(x_1,x_2)=(x_1-3{)}^2(x_2-3)+(x_1-5)(x_2-5{)}^2,$ and $x=(x_1,x_2).$ Write down the steepest

decent update for the variable $x$ when minimizing $f.$

Use the following equations to find $\frac{\text{d}\text{e}\text{l}\text{y}\text{y}\text{y}}{del{x}_2}$ at the point $(x_1,x_2)=(1,1).$

$y_1=x_1+2x_2$

$y_2=3x_1-x_2$

$y{y}_1=4y_1+5y_2$

$y{y}_2=6y_1+y_2$

$yyy=$max$\{y{y}_1,y{y}_2\}$

$($Past Exam Question from August $2017.)$ The defining equations of the output of a neural network

are as follows.

$y_i=b_i+w_{i1}{x}_1+w_{i2}{x}_2,i=1,2,$dots$9$

$y{y}_j=b{b}_j+{\displaystyle \underset{i=1}{\overset{9}{}}}w{w}_{ji}{y}_i,j=1,2,$dots$7$

$yyy=bbb+{\displaystyle \underset{i=1}{\overset{7}{}}}ww{w}_{i}y{y}_i$

Write down the back propagation update for $w_{81}.($No need to show your derivation. Try to do it using

your intuition. If you prefer use a diagram. I am only interested in your final answer.$)$