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