If z = (ax + b)(cy + d), then find \(\frac{∂z}{∂x}\) and \(\frac

1.	If z = (ax + b)(cy + d), then find \(\frac{∂z}{∂x}\) and \(\frac{∂z}{∂y}\).
Answer» Given, z = (ax + b)(cy + d) Differentiating partially with respect to x we get, \(\frac{∂z}{∂x}\) = (cy + d) \(\frac{∂}{∂x}\)(ax + b) [∵ (cy + d) is constant] = (cy + d)(a + 0) = a(cy + d) Differentiating partially with respect to y we get, \(\frac{∂z}{∂y}\) = (ax + b) \(\frac{∂}{∂y}\)(cy + d) = (ax + b)(c + 0) = c(ax + b)

If z = (ax + b)(cy + d), then find \(\frac{∂z}{∂x}\) and \(\frac{∂z}{∂y}\).

Answer»

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

Differentiating partially with respect to x we get,

\(\frac{∂z}{∂x}\) = (cy + d) \(\frac{∂}{∂x}\)(ax + b) [∵ (cy + d) is constant]

= (cy + d)(a + 0)

= a(cy + d)

Differentiating partially with respect to y we get,

\(\frac{∂z}{∂y}\) = (ax + b) \(\frac{∂}{∂y}\)(cy + d)

= (ax + b)(c + 0)

= c(ax + b)