November 13, 2012
3.8 Derivatives of Inverse Trigonometric Functions
Day 1
What is an inverse?
sin x = arcsin x
cos x = arccos x
-1
-1
tan-1x = arctan x
-
Graphs
y = sin x
sin x = 0.5
y = sin-1x
November 13, 2012
d sin-1x =
M
E dx
M
O
d cos-1x =
R
dx
I
Z
E
d tan-1x =
dx
Ex 1)
d
tan -1(x2) =
dx
1
√ 1 - x2
1
√ 1 - x2
1
1 + x2
Ex 2)
d tan -1√(3x) =
dx
November 13, 2012
Ex 3)
Ex 4)
d sin -1 x =
dx
3
d arcsin (2x7 + 1) =
dx
Ex 5)
d
dx
x cos x + √(1 - x ) =
-1
2