Preview:
Citation preview
- 1. Solution key to exercises 7.1 and 8.1 Chain Rule and
Derivatives of Trigonometric Functions
- 2. Exercises 7.1 Chain Rule Write your solutions orderly and
neatly. Techniques to remember: Product rule and Chain Rule 4
15and4Let xxgxxh 5154',2' 32/1 xxgxxh 51544152''' 342/1
xxxxhgghf
- 3. Exercises 7.1 Chain Rule 8 3324 2 12 212433312'' ' x xxxx g
hggh f
- 4. Exercises 7.1 Chain Rule Observe Chain Rule xxxxuuuuy
219216'9'6' 225225
- 5. Exercise 7.1 Chain Rule The tangent line to the curve is
horizontal means the derivative of the function at the point of
tangency is ZERO 0TLm 0TLm Analysis by graphs has limitations
- 6. Exercises 7.1 Chain Rule 042343' 22 xxxy 2042 xx 013 03434
22 xx xxxx 1,3 xx
- 7. Exercises 7.1 Chain Rule Recall the equation of a line, in
particular, the point-slope form 11 xxmyy 1,1, 11 yx 1at' xym
- 8. Exercises 7.1 Chain Rule 2' ,1at 2 22 ' 2 2212 ' 2 2/122 2
2/12 2 12 y x x xx y x xxxx y Equation of line is 121 xy
- 9. Exercises 8.1 Derivative Trigonometric Functions xxxxxf
105sec5tan1' 222 Chain rule xxxxf 211sec' 2/12 2 122
- 10. Exercises 8.1 Derivative Trigonometric Functions 11 xxmyy
0,, 11 yx xym at' 24 2 4 22 1012tansec ' x xxxx y xy 2 1
- 11. Exercise 8.1 Derivative Trigonometric Functions
- 12. Exercises 8.1 Derivative Trigonometric Functions
radians31.152.75cos 01cos4' 4 11 o x xy Solution set: The cosine
function is a periodic function! It repeats the cycle every 2pi
radians. integeranyis ,231.1 k kx
- 13. Exercises 8.1 Derivative Trigonometric Functions
0tansec4tansecsec4)('' 1sec2' 2 2 xxxxxxf xxf Kelan nagze-zero ang
second derivative? 0tanor0sec0tansec2 xxxx ,0x 180,0x