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H(z)=(6−z²)(z³−5z+3)

Use the product rule to find the derivative of the given function.

Sagot :

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Answer: (-2z)(z³−5z+3) + (6-z²)(3z²-5)

Step-by-step explanation:

The product rule is given by the formula:

[f(x)g(x)]' = f'(x)g(x) + f(x)g'(x)

For the given function:

  • f(x) = 6-z²
  • g(x) = z³−5z+3

Let's find the derivative both f(x) and g(x) using the power rule:

  • f'(x) = -2z
  • g'(x) = 3z²-5

Apply the product rule:

H'(z) = (-2z)(z³−5z+3) + (6-z²)(3z²-5)

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