Question

Derivative of f(z)=(a bz cz²)/(z²):

a) f'(z) = 2a - 2bz + 2cz
b) f'(z) = -a + bz - cz²
c) f'(z) = -2a + 2bz - 2cz
d) f'(z) = a - bz + cz²

Answer 1

The derivative of the provided function can be found using the quotient rule, resulting in f'(z) = (a(b - 2cz))/(2z^3).

Step-by-step explanation:

The derivative of the function f(z) = (abz - cz²)/(z²) can be found using the quotient rule. The quotient rule states that the derivative of a quotient of two functions is equal to the derivative of the numerator multiplied by the denominator, minus the numerator multiplied by the derivative of the denominator, all divided by the square of the denominator.

Applying the quotient rule to the given function, we have:

1. 
   
3. Derivative of numerator: a(b - 2cz)
4. 
   
6. Derivative of denominator: 2z
7. 
   
9. Square of denominator: z^4

Combining these results, we get the derivative of the function as:

f'(z) = (a(b - 2cz))/(2z^3)