State which rule or rules $($product$,$ quotient, chain$)$ you would use to find the derivative of each of the functions and why. Do not find the derivative.

$+3$

$($a$)g(x)=\frac{x^2-3x+5}{x^2}$

${\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}$

The quotient cule if used because the functions is given as a ration of two functions. It is applied when differentialins a function that is the divison of two other furctions.

$$3($b$)h(x)={10}^{x^2{e}^x}$ The product rule and the chain cule is used.

product rule since $h(x)$ is the product of two functions, ${16}^{x2}$ and $e^x,$ the product rule is a pplied to $d$ ifferentiat each put separately

Chain rule: witin ${10}^{x^2},$ the ch an rule is used hecacs it involves an exponen $\text{'}$w th $x^2,$ requirirg differcila on of the outher funcion ${10}^0($wherl $v=x^2)$

$x$

$($c$)s(t)=\frac{t^2+3}{4tln(t)}$