Syllabus Vector Differentiation - Velocity and Acceleration - Gradient ...

Engineering Mathematics - II - Vector Calculus - 2007
Page 24 of 72
g
dt
f
d
dt
d g
f
g)
( f
dt
d
4.
Proof:
k
f
j
f
i
f
f
Let 3
2
1
k
g
j
g
i
g
g 3
2
1
3
2
1
3
2
1
g
g
g
f
f
f
k
j
i
g
f
)
f
g
g
(f
i
g
f 3
2
3
2
)
f
g
g
(f
i
dt
d
g)
( f
dt
d
3
2
3
2
dt
df
g
f
dt
dg
dt
dg
f
g
dt
d f
i
3
2
3
2
3
2
3
2
dt
df
g
dt
dg
f
i
f
dt
dg
g
dt
d f
i
3
2
3
2
3
2
3
2
dt
d g
f
g
dt
f
d
dt
d h
g ,
,
f
,h
dt
d g
,
f
h
g,
,
dt
f
d
h
g,
,
f
dt
d
5.
Proof:
h
.
g
f
dt
d
h
g,
,
f
dt
d
dt
d h
.
g
f
h
.
g
f
dt
d
dt
d h
.
g
f
h
.
dt
d g
f
h
.
g
dt
f
d
dt
d h
g,
,
f
h
,
dt
d g
,
f
h
g ,
,
dt
f
d