Task $1(3$ points each$).$

A function is given:

$y=5x^{4}ln(2x)+1$

$($a$)$ Find $\frac{dy}{dx}$

$($b$)$ Find $\frac{d^{2}y}{d{x}^2}$

$($c$)$ Find $\frac{d^{3}y}{d{x}^3}$

$($d$)$ Find $\frac{d^{4}y}{d{x}^4}$

$($e$)$ Find $\frac{d^{5}y}{d{x}^5}$

$($f$)$ Find $\frac{d^{6}y}{d{x}^6}$

$($g$)$ Find $\frac{d^{7}y}{d{x}^7}$

$($h$)$ Find $\frac{d^{8}x}{d{y}^8}$