Question

Use the Chain Rule to find the indicated partial derivatives. u = x^4 + yz, x = pr sin(θ), y = pr cos(θ), z = p + r; (partial u)/(partial p), (partial u)/(partial r), (partial u)/(partial theta) when p = 3, r = 4, θ = 0

Answer #1

Use the Chain Rule to find the indicated partial
derivatives.
w = xy + yz + zx, x = r
cos(θ), y = r
sin(θ), z = rθ;
∂w
∂r
,
∂w
∂θ
when r = 4, θ =
π
2
∂w
∂r
=
∂w
∂θ
=

Use the Chain Rule to find the indicated partial
derivatives.
u =
r2 + s2
, r = y + x cos
t, s = x + y sin t
∂u
∂x
,
∂u
∂y
,
∂u
∂t
when x = 2, y =
5, t = 0

Use the Chain Rule to find the indicated partial derivatives. u
=sqrt( r^2 + s^2) , r = y + x cos(t), s = x + y sin(t)
∂u ∂x , ∂u ∂y , ∂u ∂t when x = 1, y = 4, t = 0

Use the Chain Rule to find the indicated partial derivatives. ?
= ?^ 2 + ?^ 2 , ? = ?? cos ? , ? = ?? sin ?
??/??, ??/?? , ??/?? ?ℎ?? ? = 2, ? = 3, ? = 0°

Use the Chain Rule to find the indicated partial
derivatives.
z = x2 + xy3,
x = uv2 + w3,
y = u + vew
when u = 2, v = 2, w = 0

Use the Chain Rule to find the indicated partial
derivatives.
P = sqrt(u2 + v2 +
w2), u =
xey, v =
yex, w = exy; when x=0
and y=2.
∂P
∂y
and
∂P
∂x

Use the Chain Rule to find the indicated partial
derivatives.
R = ln(u2 + v2 + w2),
u = x + 3y, v = 5x −
y, w = 2xy;
when x = y = 2
dR/dx=
dR/dy=

Use the Chain Rule to find the indicated partial
derivatives.
N =
p + q
p + r
, p = u + vw, q =
v + uw, r = w + uv;
∂N
∂u
,
∂N
∂v
,
∂N
∂w
when u = 6, v = 5, w = 7

1.
a) Use the Chain Rule to calculate the partial derivatives.
Express the answer in terms of the independent variables.
∂f
∂r
∂f
∂t
; f(x, y, z) = xy +
z2, x = r + s −
2t, y = 6rt, z =
s2
∂f
∂r
=
∂f
∂t
=
b) Use the Chain Rule to calculate the partial derivative.
Express the answer in terms of the independent variables.
∂F
∂y
; F(u, v) =
eu+v, u =
x5, v = 2xy
∂F
∂y
=
c)...

Let f(x,y,z)=xy+z^3, x=r+s−8t, y=3rt, z=s^6.
Use the Chain Rule to calculate the partial derivatives.
(Use symbolic notation and fractions where needed. Express the
answer in terms of independent variables

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