Consider the following functions of the variables u$,$ v$,$ w$.$ Assume the variables x$,$ y$,$ x$($i$)$ and y$($i$)$ are

constants, representing numbers that will not change during the execution of a machine learning algorithm

$($e$.$g$.,$ training data$).$

f $($u;v$)=10$u$2$v$3+3$v$2+4$u

g$($u;v;w$)=$ x log$($u$)+$yuvw$2+10$x$2$

h$($u;v$)=$

m$$

i$=1$

$1$

$2$

$($x$($i$)$u$+$y$($i$)$v$)2$

Please write the following partial derivatives:

$(1).$

$$u f $($u;v$)=$

$(2).$

$$ v f $($u;v$)=$

$(3).$

$$ug$($u;v;w$)=$

$(4).$

$$ vg$($u;v;w$)=$

$(5).$

$$wg$($u;v;w$)=$

$(6).$

$$uh$($u;v$)=$

$(7).$

$$ vh$($u;v$)=$