Consider the following.

$w=x-\frac{1}{y},x=e^{5t},y=t^7$

$($a$)$ Find $\frac{dw}{dt}$ by using the appropriate Chain Rule. $($Enter your answer in terms of $t.)$

$\frac{dw}{dt}=$

$($b$)$ Find $\frac{dw}{dt}$ by converting $w$ to a function of $t$ before differentiating. $($Enter your answer in terms of $t.)$

$\frac{dw}{dt}=$