Partial Derivatives

Question

Find the first partial derivatives of the function.

z = (4x + 5y)⁷

z/x=

z/y=

Answer 1

To find the partial derivatives of the function z = (4x + 5y)⁷ with respect to x and y, we can use the chain rule:

∂z/∂x = 7(4x + 5y)⁶ * 4 = 28(4x + 5y)⁶

∂z/∂y = 7(4x + 5y)⁶ * 5 = 35(4x + 5y)⁶

Hope this helped!