25 Chain Rule
Q. What is tollt oght)) informs of gif', and y'?
fox (fog) (b) = I've g(z)l-fry(s), gaz)-gow
Z-1
y(z) - g(x)
lim f(y(z)) -f(g(x)) (2)-9 (*)
g(27-9(x)
Assumes g(z) (906)
N nitely many times
= 22X
ок чех
I'm y(s) fegcoss
9(2)-5(8)
\g(2) zgus
blc g is continuous
at x
f'(g(x))· g'(x)
2-x
ޔ
2-
lim y(z) ~g(x)
y(2)-9
Diff custbont
for g(x)
The Chain Rule
y is differentiable at x; and f is differentiable at g(x), then
If yj
d
Ax (fogkas = f(glass- g'(x)
Alternatiudy, if ve write yafcul and
where you is evaluated at
Examples: I ₤ (tan (8/32+))
ત
2
(sec² (8x² +2x)-(24x² + 2)
u= g(x)
u=
dx
(g(x) then do you have
fan) = tance) 2 ₤1 (5x-76-3/137)
43
883+2×
ご
=137 (5x-3-2) (5-14x)
Ju
fi fl fi fi
Q. What is tollt oght)) informs of gif', and y'?
fox (fog) (b) = I've g(z)l-fry(s), gaz)-gow
Z-1
y(z) - g(x)
lim f(y(z)) -f(g(x)) (2)-9 (*)
g(27-9(x)
Assumes g(z) (906)
N nitely many times
= 22X
ок чех
I'm y(s) fegcoss
9(2)-5(8)
\g(2) zgus
blc g is continuous
at x
f'(g(x))· g'(x)
2-x
ޔ
2-
lim y(z) ~g(x)
y(2)-9
Diff custbont
for g(x)
The Chain Rule
y is differentiable at x; and f is differentiable at g(x), then
If yj
d
Ax (fogkas = f(glass- g'(x)
Alternatiudy, if ve write yafcul and
where you is evaluated at
Examples: I ₤ (tan (8/32+))
ત
2
(sec² (8x² +2x)-(24x² + 2)
u= g(x)
u=
dx
(g(x) then do you have
fan) = tance) 2 ₤1 (5x-76-3/137)
43
883+2×
ご
=137 (5x-3-2) (5-14x)
Ju
fi fl fi fi
