2.4 chain rule
TRANSCRIPT
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2.4 The Chain Rule
"I recoil with dismay and horror at thislamentable plague of functions which do not
have derivatives. -- Charles Hermite
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Objectives:
To find derivatives using the chain rule
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A third way…
Chain rule
y ! deriv of outside #eep inside same$ times derivof inside
%&le'
)('))((''
))((
x g x g f y
x g f y
==
2)56( −= x y
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Ea!"le
2)12( += x y
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Another ea!"le
32 )1( += x y
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#hat about tri$ functions%
Thin# of u substitution
x x f 2sin)( =
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&ou try:
32)23( x x y −= 5)(sin x y =
)sin( 5
x y = 4
)( Bobdx
d
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'ore challen$in$ ea!"les…
3 22 )1( −= x y
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Another one
2)32(
7)(−−=
x x g )hat rules will we use*
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&et one !ore…
22 1 x x y −=
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Review:
Chain +ule'
)()('
)(
1 quantityof derivquantityk n y
quantityk y
n
n
−
•=
=
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2 !ore ea!"les
3 2 4+=
x
x y
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Tri$ Chain Rule
,eriv of trig #eep angle same$ deriv of angle
e careful of double chain rule
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Ea!"le
x y 2sin41 2=
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Another ea!"le
t y 4sin3=
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Three ty"es…
)3cos( 2 x y = 2)3cos( x y =
2))3(cos( x y =