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QUESTION 14 Suppose $x = s^2$, $y = st$ and $z = tu$. The function $W = f(x,y,z)$ has the partial derivatives $W_x = W_y = W_z = 4$ $W_{xx} = W_{yy} = W_{zz} = W_{xy} = W_{xz} = W_{yz} = 1$ at the point $(x,y,z) = (4,7,1)$. Find $W_{ss}$ at that point.

          QUESTION 14
Suppose $x = s^2$, $y = st$ and $z = tu$.
The function $W = f(x,y,z)$ has the partial derivatives
$W_x = W_y = W_z = 4$
$W_{xx} = W_{yy} = W_{zz} = W_{xy} = W_{xz} = W_{yz} = 1$
at the point $(x,y,z) = (4,7,1)$.
Find $W_{ss}$ at that point.

QUESTION 14
Suppose x = s^2, y = st and z = tu.
The function W = f(x,y,z) has the partial derivatives
Wx = Wy = Wz = 4
Wxx = Wyy = Wzz = Wxy = Wxz = Wyz = 1
at the point (x,y,z) = (4,7,1).
Find Wss at that point.

Added by Chelsea S.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Adi S

09/03/2023

Step 1

First, we need to use the given partial derivatives to find the second-order partial derivatives: Wxx = WxxxX + WxxyY + WxxzZ = WxxX Wyy = WxyxX + WyyyY + WyyzZ = WyyY Wzz = WxzxX + WyzY + WzzzZ = WzzZ Wxy = WxyX + WyyY + WxyzZ = WxyX Wxz = WxxX + WyzY + WxzzZ = Show more…

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Suppose X = s^2, y = St and 2 = tu^2 The function W = f(x, V, 2) has the partial derivatives Wx = Wy = Wz = Wxx = Wyt = Wzz = Wxy = Wxz = Wyz = at the point (x, V, 2) = (4, 7, 1). Find Wss at that point: