$Q1$: $We$ learned $in$ class that $ify=f(x)g(x),we$ can use the product rule $to$ take the derivative and get that

$y^{\text{'}}=f^{\text{'}}(x)g(x)+f(x)g^{\text{'}}(x).$ However, $ifwe$ didn't already know this formula, $we$ could use logarithmic

differentiation $to$ find $it!So$ the goal $of$ this problem $is$ for you $to$ use logarithmic differentiation $to$

rediscover the product rule $by$ doing the following:

$(1)$ First, take the natural $logof$ both sides $of$ the equation $y=f(x)g(x).$

$(2)$ Second, use a $log$ rule $to$ break apart the product $f(x)g(x).$

$(3)$ Finally, use implicit differentiation $to$ solve for $y^{\text{'}}.$