To find the rate of change in z with respect to x, we need to take the partial derivative of z with respect to x while holding y fixed:
∂z/∂x = ∂/∂x (√2x + 5y)
Using the chain rule, we have:
∂z/∂x = ∂/∂x (√2x) = (√2)(1) = √2
So the rate of change in z with respect to x, while holding y fixed, is √2.
To find the rate of change in z with respect to y, we need to take the partial derivative of z with respect to y while holding x fixed:
∂z/∂y = ∂/∂y (√2x + 5y)
Using the chain rule, we have:
∂z/∂y = ∂/∂y (5y) = 5
So the rate of change in z with respect to y, while holding x fixed, is 5.
Let z=√2x+5y
. Then:
The rate of change in z
at (2,4)
as we change x
but hold y
fixed is
, and
The rate of change in z
at (2,4)
as we change y
but hold x
fixed is
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