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13.2 Derivatives and Integrals of Vector Functions
The derivative of a vector function
()
, ()
tf
t
g
t
h
t
=
r
is
'
'
,
'
, '
t
g
t
h
t
=
r
. Note
that you differentiate each component separately. For example, look at the 2dimensional space curve
defined by
4s
in
, 2cos
tt
=−
t
r
. If
r
is the position function of a particle, then
r
is
the velocity function,
like the velocity function in one dimension.
t
'( )
t
Let's look at a geometric description of the derivative
r
. The derivative
r
is tangent to the
space curve
r
.
t
t
t
2
1
1
2
0.5
0.5
1
The figure shown above is the curve
2s
,cos
r
t
with the derivative vector
2 cos( ),
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This note was uploaded on 01/20/2012 for the course MATH 2057 taught by Professor Estrada during the Fall '08 term at LSU.
 Fall '08
 Estrada
 Derivative, Integrals

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