Question

H(z)=(1+2z+3z^2) (5z+8z^2-2^3) in product rule?

Answer 1

To find the derivative of h(z) = (1 + 2z + 3z^2)(5z + 8z^2 - 2^3) using the product rule, differentiate each term and apply the product rule.

Step-by-step explanation:

The given function is: h(z) = (1 + 2z + 3z^2)(5z + 8z^2 - 2^3)

To find the derivative of h(z) using the product rule, we need to differentiate each term:

1. Derivative of (1 + 2z + 3z^2): 2 + 6z
2. Derivative of (5z + 8z^2 - 2^3): 5 + 16z

Now, using the product rule:

h'(z) = (2 + 6z)(5z + 8z^2 - 2^3) + (1 + 2z + 3z^2)(5 + 16z)

Simplifying further, we get:

h'(z) = 10z + 16z^2 + 30z^2 + 48z - 16