Question

If z = (ax + b) (cy + d), then find `(∂z)/(∂x)` and `(∂z)/(∂y)`.

Answer 1

Given, z = (ax + b) (cy + d)

Differentiating partially with respect to x we get,

`(∂z)/(∂x) = ("c"y + "d") ∂/(∂x) ("a"x + "b")`   ...[∵ (cy + d) is constant]

= (cy + d) (a + 0)

= a(cy + d)

Differentiating partially with respect to y we get,

`(∂z)/(∂y) = ("a"x + "b") (∂)/(∂y)`(cy + d)

= (ax + b)(c + 0)

= c(ax + b)