Find the derivative the following ways.

a$.$ Using the Product Rule.

b$.$ By expanding the product first. Verify that your answer agrees with part $($a$).$

$h(z)=(z^3-3z^{2}5z)(z-7)$

a$.$ Use the Product Rule to find the derivative of the given function. Select the correct choice and $5$ li in the answer box$($es$)$ to complete your choice.

A$.$ The derivative is $(z-7)(z^3-3z^{2}5z).$

B$.$ The derivative is $(z-7)(z^3-3z^{2}5z)().$

C$.$ The derivative is $(z-7).$

D$.$ The derivative is $).$

E$.$ The derivative is $(z-7)(z^3-3z^{2}5z).$