brightness changes $by+-0\mathrm{.}35.$ Using this information, the brightness $of$ the star $at$ time $t,$ where $tis$ measured $in$ days, has been modeled $by$ the function

$B(t)=4\mathrm{.}0+0\mathrm{.}35sin(\frac{2t}{4\mathrm{.}6})$

$(a)$ Find the rate $of$ change $of$ the brightness $at$ time $t$ days.

$\frac{dB}{dt}=$

$(b)$ Find the rate $of$ change $of$ brightness $at$ time $t=4$ days.

$\frac{dB}{dt}=$