Find the first partial derivatives of the function. f(x,y) = (ax + by)/ (cx + dy)?

Solution:

f (x, y) = (ax + by)/ (cx + dy) [Given]

Now partially differentiate the function with respect to x

d(f(x, y)) / dx = d (ax + by cx + dy) / dx

= a + bcy + 0

Now partially differentiate the function with respect to y

d(f(x, y)) / dy = d(ax + by cx + dy) / dy

= 0 + bcx + d

Therefore, the first partial derivatives of the function are (a + bcy) and (bcx + d).

Find the first partial derivatives of the function. f(x,y) =  (ax + by)/ (cx + dy) ?

Summary:

The first partial derivatives of the function f (x, y) = (ax + by)/ (cx + dy) are (a + bcy) and (bcx + d).