Final answer:
The partial derivatives of z = 7xyz with respect to x and y are 7yz and 7xz respectively.
Step-by-step explanation:
To find the partial derivatives ∂z/∂x and ∂z/∂y when the function is given by z = 7xyz, we use the rules of partial differentiation.
Finding ∂z/∂x:
To find ∂z/∂x, we treat y as a constant and differentiate z with respect to x:
∂z/∂x = 7y * (d/dx) x * z = 7yz
Finding ∂z/∂y:
To find ∂z/∂y, we treat x as a constant and differentiate z with respect to y:
∂z/∂y = 7x * (d/dy) y * z = 7xz