11x1 t10 03 second derivative (2011)
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The Second Derivative
The Second Derivative
2
2
2
2
,,,dx
ydxf
dx
dxfy
The Second Derivative
2
2
2
2
,,,dx
ydxf
dx
dxfy
23 e.g. 2 xxyi
The Second Derivative
2
2
2
2
,,,dx
ydxf
dx
dxfy
23 e.g. 2 xxyi
16 xdx
dy
The Second Derivative
2
2
2
2
,,,dx
ydxf
dx
dxfy
23 e.g. 2 xxyi
16 xdx
dy
62
2
dx
yd
The Second Derivative
2
2
2
2
,,,dx
ydxf
dx
dxfy
23 e.g. 2 xxyi
16 xdx
dy
62
2
dx
yd
32 xyii
The Second Derivative
2
2
2
2
,,,dx
ydxf
dx
dxfy
23 e.g. 2 xxyi
16 xdx
dy
62
2
dx
yd
32 xyii
21
2 3 x
The Second Derivative
2
2
2
2
,,,dx
ydxf
dx
dxfy
23 e.g. 2 xxyi
16 xdx
dy
62
2
dx
yd
32 xyii
21
2 3 x
xxdx
dy23
2
12
12
The Second Derivative
2
2
2
2
,,,dx
ydxf
dx
dxfy
23 e.g. 2 xxyi
16 xdx
dy
62
2
dx
yd
32 xyii
21
2 3 x
xxdx
dy23
2
12
12
2
12 3
xx
The Second Derivative
2
2
2
2
,,,dx
ydxf
dx
dxfy
23 e.g. 2 xxyi
16 xdx
dy
62
2
dx
yd
32 xyii
21
2 3 x
xxdx
dy23
2
12
12
2
12 3
xx
13232
12
122
32
2
2
xxxx
dx
yd
The Second Derivative
2
2
2
2
,,,dx
ydxf
dx
dxfy
23 e.g. 2 xxyi
16 xdx
dy
62
2
dx
yd
32 xyii
21
2 3 x
xxdx
dy23
2
12
12
2
12 3
xx
13232
12
122
32
2
2
xxxx
dx
yd
2
122
322 33
xxx
The Second Derivative
2
2
2
2
,,,dx
ydxf
dx
dxfy
23 e.g. 2 xxyi
16 xdx
dy
62
2
dx
yd
32 xyii
21
2 3 x
xxdx
dy23
2
12
12
2
12 3
xx
13232
12
122
32
2
2
xxxx
dx
yd
2
122
322 33
xxx
33 222
32
xxx
The Second Derivative
2
2
2
2
,,,dx
ydxf
dx
dxfy
23 e.g. 2 xxyi
16 xdx
dy
62
2
dx
yd
32 xyii
21
2 3 x
xxdx
dy23
2
12
12
2
12 3
xx
13232
12
122
32
2
2
xxxx
dx
yd
2
122
322 33
xxx
33 222
32
xxx
33
322
xx
Exercise 10D; 1 to 13, every 2nd in all
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