Find the first partial derivatives of the function. f(x, y) = ax + by cx + dy
Partial differentiation means, differentiating with respect to a single variable while keeping other variables as constants in the expression.
Answer: Partially differentiating the function with respect to x and y, we get (a + bcy) and (bcx + d) respectively.
Let us go through the steps to find the partial differentiation of the given expression.
Given, f(x, y) = ax + by cx + dy
Partially differentiating the function w.r.t to x
d(f(x, y)) / dx = d(ax + by cx + dy) / dx
= a + bcy + 0
Partially differentiating w.r.t to y
d(f(x, y)) / dy = d(ax + by cx + dy) / dy
= 0 + bcx + d