Question

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

Answer #1

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Solutions Given: N18,9,0) and p (4, V,w) O(u,v,W), 8(vw) , P = utvw q = VHU W Y - W+UV When: 0=6, V=5, W=F value Given a the n of U, V, W : substitute U= G, V = 5, W = 7 bin l. q., and & so, 2 P = 6+ 5.7 = 4 q= 5 + 67 = 47 _D = 7+ 65 = 37 using chân Ist find rule- 8=37

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.
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. 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

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°

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)...

Use the Chain Rule to evaluate the partial derivative
∂f∂u and ∂f∂u at (u, v)=(−1, −1), where
f(x, y, z)=x10+yz16,
x=u2+v, y=u+v2, z=uv.
(Give your answer as a whole or exact number.)
∂f∂u=
∂f∂v=

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