for z = 13. dt f(x, y), x = g(t), y = h(t) dz 14. for z = f(u, v, w), u = g(t), v = h(t), w = k(t) dt dw for w = and h(x, у, 2), х 3D fuu, υ) , y = gu, υ) . 15. k(и, v) dw and 16. dx for w = f(r, s, 1), r= g(x, y), ду s = h(x, y), t = k(x, y) aw dw 17. and du for w = g(x, y), x = h(u, v), y = k(u, v) dw 18. and ax k(x, y) for w = E g(и, v), и %3 h(x, у), v %3D dz and for z = fx, y), х %—D 8(, 5), у%3D ht, s) 19. at ds ду 20. for y = f(u), u = g(r, s) aw and ds 21. for w = 8(и), и %3D h(s, t) 22. f(x, y, z, v), х — g(p, q). у %3D h(р, Ф), for w = op z = j(p, q), v = k(p, q) dw and dr 23. for w = f(x, y), x = g(r), y = h(s) ds dw 24. for w = g(x, y), x = h(r, s, t), y = k(r, s, t) W 3= ds
for z = 13. dt f(x, y), x = g(t), y = h(t) dz 14. for z = f(u, v, w), u = g(t), v = h(t), w = k(t) dt dw for w = and h(x, у, 2), х 3D fuu, υ) , y = gu, υ) . 15. k(и, v) dw and 16. dx for w = f(r, s, 1), r= g(x, y), ду s = h(x, y), t = k(x, y) aw dw 17. and du for w = g(x, y), x = h(u, v), y = k(u, v) dw 18. and ax k(x, y) for w = E g(и, v), и %3 h(x, у), v %3D dz and for z = fx, y), х %—D 8(, 5), у%3D ht, s) 19. at ds ду 20. for y = f(u), u = g(r, s) aw and ds 21. for w = 8(и), и %3D h(s, t) 22. f(x, y, z, v), х — g(p, q). у %3D h(р, Ф), for w = op z = j(p, q), v = k(p, q) dw and dr 23. for w = f(x, y), x = g(r), y = h(s) ds dw 24. for w = g(x, y), x = h(r, s, t), y = k(r, s, t) W 3= ds
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Question
In Exercises 13–24, draw a dependency diagram and write a Chain Rule formula for each derivative.
![for z =
13.
dt
f(x, y), x = g(t), y = h(t)
dz
14.
for z =
f(u, v, w), u = g(t), v = h(t), w = k(t)
dt
dw
for w =
and
h(x, у, 2), х 3D
fuu, υ) , y = gu, υ) .
15.
k(и, v)
dw
and
16.
dx
for w = f(r, s, 1), r= g(x, y),
ду
s = h(x, y),
t = k(x, y)
aw
dw
17.
and
du
for w = g(x, y), x = h(u, v), y = k(u, v)
dw
18.
and
ax
k(x, y)
for w =
E g(и, v), и %3
h(x, у), v %3D
dz
and
for z =
fx, y), х %—D 8(, 5), у%3D ht, s)
19.
at
ds
ду
20.
for y = f(u), u = g(r, s)
aw
and
ds
21.
for w =
8(и), и %3D h(s, t)
22.
f(x, y, z, v), х — g(p, q). у %3D h(р, Ф),
for w =
op
z = j(p, q), v = k(p, q)
dw
and
dr
23.
for w =
f(x, y), x = g(r),
y = h(s)
ds
dw
24.
for w = g(x, y),
x = h(r, s, t), y = k(r, s, t)
W 3=
ds](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fad153a8a-2318-4f42-8c16-a112ed8847a3%2F28f0c1db-6e4d-4c09-9813-6d4af923f61f%2Fsczeeza.png&w=3840&q=75)
Transcribed Image Text:for z =
13.
dt
f(x, y), x = g(t), y = h(t)
dz
14.
for z =
f(u, v, w), u = g(t), v = h(t), w = k(t)
dt
dw
for w =
and
h(x, у, 2), х 3D
fuu, υ) , y = gu, υ) .
15.
k(и, v)
dw
and
16.
dx
for w = f(r, s, 1), r= g(x, y),
ду
s = h(x, y),
t = k(x, y)
aw
dw
17.
and
du
for w = g(x, y), x = h(u, v), y = k(u, v)
dw
18.
and
ax
k(x, y)
for w =
E g(и, v), и %3
h(x, у), v %3D
dz
and
for z =
fx, y), х %—D 8(, 5), у%3D ht, s)
19.
at
ds
ду
20.
for y = f(u), u = g(r, s)
aw
and
ds
21.
for w =
8(и), и %3D h(s, t)
22.
f(x, y, z, v), х — g(p, q). у %3D h(р, Ф),
for w =
op
z = j(p, q), v = k(p, q)
dw
and
dr
23.
for w =
f(x, y), x = g(r),
y = h(s)
ds
dw
24.
for w = g(x, y),
x = h(r, s, t), y = k(r, s, t)
W 3=
ds
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