Final answer:
To find the first partial derivatives of the function z = (4x + 8y)¹¹ with respect to x and y, we use the power rule and treat the other variable as a constant.
Step-by-step explanation:
To find the first partial derivatives of the function z = (4x + 8y)¹¹, we differentiate with respect to x and y separately.
For the partial derivative with respect to x, we treat y as a constant and use the power rule:
∂z/∂x = 11(4x + 8y)¹⁰ * 4 = 44(4x + 8y)¹⁰
For the partial derivative with respect to y, we treat x as a constant and again apply the power rule:
∂z/∂y = 11(4x + 8y)¹⁰ * 8 = 88(4x + 8y)¹⁰