5.6--Inverse Trig Derivatives
Where are the inverse functions defined???
-90o ≤ sin-1x ≤ 90o
-90o ≤ tan-1x ≤ 90o
0o ≤ cos-1x ≤ 180o
How come???
Evaluate without using a calculator:
1)
tan (sin-1(-5/12))
2)
cos (cot-1(-6/7))
3)
tan (sec-1(-11/3))
4)
sin (sin-1(4/9))
1
5.6--Inverse Trig Derivatives
All 6 formulas can be proven:
y = sin-1x
2
5.6--Inverse Trig Derivatives
Find dy/dx:
5)
y = 3 tan-1 (x + 4)
7)
y = x2 tan-1(5x)
6)
y = sin-1 (6x)
Textbook problems--p. 380
Find dy/dx:
56)
y = ½ [x
4 - x2 + 4 arcsin (x/2)]
3
5.6--Inverse Trig Derivatives
Textbook problems--p. 380
Find dy/dx:
58)
2
y = x arctan 2x - ¼ ln (1 + 4x )
Find the relative extrema:
74)
y = arcsin x - 2x
4
5.6--Inverse Trig Derivatives
Textbook problems--p. 381
99)
5