12x1 t02 01 differentiating exponentials (2011)
DESCRIPTION
TRANSCRIPT
![Page 1: 12X1 T02 01 differentiating exponentials (2011)](https://reader034.vdocuments.us/reader034/viewer/2022042613/547a5f9e5806b580048b483b/html5/thumbnails/1.jpg)
Exponentials
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Exponentialsy
x
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Exponentialsy
x
1
1
aay x
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Exponentialsy
x
1
1
aay x
10
aay x
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Exponentialsy
x
1
1
aay x
10
aay x
10
aay x
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Exponentialsy
x
1
1
aay x
10
aay x
10
aay x
1
aay x
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Exponentialsy
x
1
1
aay x
10
aay x
x real all:domain
10
aay x
1
aay x
![Page 8: 12X1 T02 01 differentiating exponentials (2011)](https://reader034.vdocuments.us/reader034/viewer/2022042613/547a5f9e5806b580048b483b/html5/thumbnails/8.jpg)
Exponentialsy
x
1
1
aay x
10
aay x
x real all:domain0:range y
10
aay x
1
aay x
![Page 9: 12X1 T02 01 differentiating exponentials (2011)](https://reader034.vdocuments.us/reader034/viewer/2022042613/547a5f9e5806b580048b483b/html5/thumbnails/9.jpg)
Exponentialsy
x
1
1
aay x
10
aay x
x real all:domain0:range y
10
aay x
1
aay x
xey
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Exponentialsy
x
1
1
aay x
10
aay x
x real all:domain0:range y
10
aay x
1
aay x
xey
e is an irrational number, it is defined as; n
n
n
11lim
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Exponentialsy
x
1
1
aay x
10
aay x
x real all:domain0:range y
10
aay x
1
aay x
xey
e is an irrational number, it is defined as; n
n
n
11lim
718281828.2e
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Exponentialsy
x
1
1
aay x
10
aay x
x real all:domain0:range y
10
aay x
1
aay x
xey
e is an irrational number, it is defined as; n
n
n
11lim
718281828.2edp) 3 (to 086.20 e.g. 3 e
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Differentiating Exponentials
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Differentiating Exponentials
xfey
![Page 15: 12X1 T02 01 differentiating exponentials (2011)](https://reader034.vdocuments.us/reader034/viewer/2022042613/547a5f9e5806b580048b483b/html5/thumbnails/15.jpg)
Differentiating Exponentials
xfey
xfexfdxdy
![Page 16: 12X1 T02 01 differentiating exponentials (2011)](https://reader034.vdocuments.us/reader034/viewer/2022042613/547a5f9e5806b580048b483b/html5/thumbnails/16.jpg)
Differentiating Exponentials
xfey
xfexfdxdy
xfay
![Page 17: 12X1 T02 01 differentiating exponentials (2011)](https://reader034.vdocuments.us/reader034/viewer/2022042613/547a5f9e5806b580048b483b/html5/thumbnails/17.jpg)
Differentiating Exponentials
xfey
xfexfdxdy
xfay
xfaaxfdxdy log
![Page 18: 12X1 T02 01 differentiating exponentials (2011)](https://reader034.vdocuments.us/reader034/viewer/2022042613/547a5f9e5806b580048b483b/html5/thumbnails/18.jpg)
Differentiating Exponentials
xfey
xfexfdxdy
xfay
xfaaxfdxdy log
xeyi e.g.
![Page 19: 12X1 T02 01 differentiating exponentials (2011)](https://reader034.vdocuments.us/reader034/viewer/2022042613/547a5f9e5806b580048b483b/html5/thumbnails/19.jpg)
Differentiating Exponentials
xfey
xfexfdxdy
xfay
xfaaxfdxdy log
xeyi e.g.xe
dxdy
![Page 20: 12X1 T02 01 differentiating exponentials (2011)](https://reader034.vdocuments.us/reader034/viewer/2022042613/547a5f9e5806b580048b483b/html5/thumbnails/20.jpg)
Differentiating Exponentials
xfey
xfexfdxdy
xfay
xfaaxfdxdy log
xeyi e.g.xe
dxdy
xeyii 5
![Page 21: 12X1 T02 01 differentiating exponentials (2011)](https://reader034.vdocuments.us/reader034/viewer/2022042613/547a5f9e5806b580048b483b/html5/thumbnails/21.jpg)
Differentiating Exponentials
xfey
xfexfdxdy
xfay
xfaaxfdxdy log
xeyi e.g.xe
dxdy
xeyii 5
xedxdy 55
![Page 22: 12X1 T02 01 differentiating exponentials (2011)](https://reader034.vdocuments.us/reader034/viewer/2022042613/547a5f9e5806b580048b483b/html5/thumbnails/22.jpg)
Differentiating Exponentials
xfey
xfexfdxdy
xfay
xfaaxfdxdy log
xeyi e.g.xe
dxdy
xeyii 5
xedxdy 55
34 xeyiii
![Page 23: 12X1 T02 01 differentiating exponentials (2011)](https://reader034.vdocuments.us/reader034/viewer/2022042613/547a5f9e5806b580048b483b/html5/thumbnails/23.jpg)
Differentiating Exponentials
xfey
xfexfdxdy
xfay
xfaaxfdxdy log
xeyi e.g.xe
dxdy
xeyii 5
xedxdy 55
34 xeyiii344 xe
dxdy
![Page 24: 12X1 T02 01 differentiating exponentials (2011)](https://reader034.vdocuments.us/reader034/viewer/2022042613/547a5f9e5806b580048b483b/html5/thumbnails/24.jpg)
Differentiating Exponentials
xfey
xfexfdxdy
xfay
xfaaxfdxdy log
xeyi e.g.xe
dxdy
xeyii 5
xedxdy 55
34 xeyiii344 xe
dxdy
232
xxeyiv
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Differentiating Exponentials
xfey
xfexfdxdy
xfay
xfaaxfdxdy log
xeyi e.g.xe
dxdy
xeyii 5
xedxdy 55
34 xeyiii344 xe
dxdy
232
xxeyiv
232
32 xxexdxdy
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(v) xexy 423
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(v) xexy 423
xeexdxdy xx 643 442
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(v) xexy 423
xeexdxdy xx 643 442
126612
4
442
xxexeex
x
xx
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(v) xexy 423
xeexdxdy xx 643 442
126612
4
442
xxexeex
x
xx
73 2 xe yvi
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(v) xexy 423
xeexdxdy xx 643 442
126612
4
442
xxexeex
x
xx
73 2 xe yvi
xx eedxdy 363 327
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(v) xexy 423
xeexdxdy xx 643 442
126612
4
442
xxexeex
x
xx
73 2 xe yvi
xx eedxdy 363 327
633 221 xx ee
![Page 32: 12X1 T02 01 differentiating exponentials (2011)](https://reader034.vdocuments.us/reader034/viewer/2022042613/547a5f9e5806b580048b483b/html5/thumbnails/32.jpg)
(v) xexy 423
xeexdxdy xx 643 442
126612
4
442
xxexeex
x
xx
73 2 xe yvi
xx eedxdy 363 327
633 221 xx ee
3
x
x
eeyvii
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(v) xexy 423
xeexdxdy xx 643 442
126612
4
442
xxexeex
x
xx
73 2 xe yvi
xx eedxdy 363 327
633 221 xx ee
3
x
x
eeyvii
23
3
x
xxxx
eeeee
dxdy
![Page 34: 12X1 T02 01 differentiating exponentials (2011)](https://reader034.vdocuments.us/reader034/viewer/2022042613/547a5f9e5806b580048b483b/html5/thumbnails/34.jpg)
(v) xexy 423
xeexdxdy xx 643 442
126612
4
442
xxexeex
x
xx
73 2 xe yvi
xx eedxdy 363 327
633 221 xx ee
3
x
x
eeyvii
23
3
x
xxxx
eeeee
dxdy
2
2
22
33
33
x
x
x
xxx
eee
eee
![Page 35: 12X1 T02 01 differentiating exponentials (2011)](https://reader034.vdocuments.us/reader034/viewer/2022042613/547a5f9e5806b580048b483b/html5/thumbnails/35.jpg)
(v) xexy 423
xeexdxdy xx 643 442
126612
4
442
xxexeex
x
xx
73 2 xe yvi
xx eedxdy 363 327
633 221 xx ee
3
x
x
eeyvii
23
3
x
xxxx
eeeee
dxdy
2
2
22
33
33
x
x
x
xxx
eee
eee
1,1point at the
1 o tangent t theFind 2
2
eeyviii x
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(v) xexy 423
xeexdxdy xx 643 442
126612
4
442
xxexeex
x
xx
73 2 xe yvi
xx eedxdy 363 327
633 221 xx ee
3
x
x
eeyvii
23
3
x
xxxx
eeeee
dxdy
2
2
22
33
33
x
x
x
xxx
eee
eee
1,1point at the
1 o tangent t theFind 2
2
eeyviii x
x
x
edxdy
ey
2
2
2
1
![Page 37: 12X1 T02 01 differentiating exponentials (2011)](https://reader034.vdocuments.us/reader034/viewer/2022042613/547a5f9e5806b580048b483b/html5/thumbnails/37.jpg)
(v) xexy 423
xeexdxdy xx 643 442
126612
4
442
xxexeex
x
xx
73 2 xe yvi
xx eedxdy 363 327
633 221 xx ee
3
x
x
eeyvii
23
3
x
xxxx
eeeee
dxdy
2
2
22
33
33
x
x
x
xxx
eee
eee
1,1point at the
1 o tangent t theFind 2
2
eeyviii x
x
x
edxdy
ey
2
2
2
1
22,1when edxdyx
![Page 38: 12X1 T02 01 differentiating exponentials (2011)](https://reader034.vdocuments.us/reader034/viewer/2022042613/547a5f9e5806b580048b483b/html5/thumbnails/38.jpg)
(v) xexy 423
xeexdxdy xx 643 442
126612
4
442
xxexeex
x
xx
73 2 xe yvi
xx eedxdy 363 327
633 221 xx ee
3
x
x
eeyvii
23
3
x
xxxx
eeeee
dxdy
2
2
22
33
33
x
x
x
xxx
eee
eee
1,1point at the
1 o tangent t theFind 2
2
eeyviii x
x
x
edxdy
ey
2
2
2
1
22,1when edxdyx
121 22 xeey
![Page 39: 12X1 T02 01 differentiating exponentials (2011)](https://reader034.vdocuments.us/reader034/viewer/2022042613/547a5f9e5806b580048b483b/html5/thumbnails/39.jpg)
(v) xexy 423
xeexdxdy xx 643 442
126612
4
442
xxexeex
x
xx
73 2 xe yvi
xx eedxdy 363 327
633 221 xx ee
3
x
x
eeyvii
23
3
x
xxxx
eeeee
dxdy
2
2
22
33
33
x
x
x
xxx
eee
eee
1,1point at the
1 o tangent t theFind 2
2
eeyviii x
x
x
edxdy
ey
2
2
2
1
22,1when edxdyx
121 22 xeey
012221
22
222
eyxeexeey
![Page 40: 12X1 T02 01 differentiating exponentials (2011)](https://reader034.vdocuments.us/reader034/viewer/2022042613/547a5f9e5806b580048b483b/html5/thumbnails/40.jpg)
2
4 xyix
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2
44log2 xxdxdy
2
4 xyix
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2
44log2 xxdxdy
2
4 xyix x yx log
![Page 43: 12X1 T02 01 differentiating exponentials (2011)](https://reader034.vdocuments.us/reader034/viewer/2022042613/547a5f9e5806b580048b483b/html5/thumbnails/43.jpg)
2
44log2 xxdxdy
2
4 xyix x yx logyex
![Page 44: 12X1 T02 01 differentiating exponentials (2011)](https://reader034.vdocuments.us/reader034/viewer/2022042613/547a5f9e5806b580048b483b/html5/thumbnails/44.jpg)
2
44log2 xxdxdy
2
4 xyix x yx logyex ye
dydx
![Page 45: 12X1 T02 01 differentiating exponentials (2011)](https://reader034.vdocuments.us/reader034/viewer/2022042613/547a5f9e5806b580048b483b/html5/thumbnails/45.jpg)
2
44log2 xxdxdy
2
4 xyix x yx logyex ye
dydx
yedxdy 1
![Page 46: 12X1 T02 01 differentiating exponentials (2011)](https://reader034.vdocuments.us/reader034/viewer/2022042613/547a5f9e5806b580048b483b/html5/thumbnails/46.jpg)
2
44log2 xxdxdy
2
4 xyix x yx logyex ye
dydx
yedxdy 1
x1
![Page 47: 12X1 T02 01 differentiating exponentials (2011)](https://reader034.vdocuments.us/reader034/viewer/2022042613/547a5f9e5806b580048b483b/html5/thumbnails/47.jpg)
2
44log2 xxdxdy
Exercise 13A; 1 to 4 ace etc, 6 to 8 ace, 10 to 12 ac
Exercise 13B; 4, 7, 8 to 22 evens (not 18)
2
4 xyix x yx logyex ye
dydx
yedxdy 1
x1