a. Use the product rule to find the derivative of the given function.
b. Find the derivative by expanding the product first.
\[
h(z)=\left(7-z^{2}\right)\left(z^{3}-4 z+5\right)
\]

Step 1 ：Given the function \(h(z) = (7 - z^2)(z^3 - 4z + 5)\), we need to find its derivative.

Step 2 ：First, identify the two functions that are being multiplied together. Here, \(f(z) = 7 - z^2\) and \(g(z) = z^3 - 4z + 5\).

Step 3 ：Next, find the derivatives of \(f(z)\) and \(g(z)\). The derivative of \(f(z)\) is \(f'(z) = -2z\), and the derivative of \(g(z)\) is \(g'(z) = 3z^2 - 4\).

Step 4 ：Then, apply the product rule, which states that the derivative of the product of two functions is the derivative of the first function times the second function plus the first function times the derivative of the second function.

Step 5 ：Applying the product rule, we get \(h'(z) = f'(z)g(z) + f(z)g'(z) = -2z(z^3 - 4z + 5) + (7 - z^2)(3z^2 - 4)\).

Step 6 ：Finally, the derivative of the function \(h(z) = (7 - z^2)(z^3 - 4z + 5)\) is \(\boxed{-2z(z^3 - 4z + 5) + (7 - z^2)(3z^2 - 4)}\).