Partial Derivatives

Question

Find the first partial derivatives of the function.

g(x, y) = 5 ln(4x + ln y)

Answer 1

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

∂g/∂x = 5/[4x+ln(y)] * 4 = 20/[4x+ln(y)]

∂g/∂y = 5/[4x+ln(y)] * 1/y = 5/[4xy+y·ln(y)]

Hope this helped!