Question

Differentiate the function. r(z) = z−3 − z1/2

Answer 1

To differentiate the function r(z) = z−3 − z1/2, we use the power rule. The derivative of the first term is -3z^-4, and the derivative of the second term is (1/2)z^-1/2. Combining the derivatives gives r'(z) = -3z^-4 - (1/2)z^-1/2.

Step-by-step explanation:

To differentiate the function r(z) = z−3 − z1/2, we can use the power rule of differentiation. Let's break it down step by step:

1. For the first term, z-3, the derivative is -3z-4 using the power rule.
2. For the second term, z1/2, the derivative is (1/2)z-1/2 using the power rule.

Combining the derivatives of both terms, we get:

r'(z) = -3z-4 - (1/2)z-1/2