Transcript Section 3.6

Section 3.6
Derivatives of Inverse Functions
Derivatives of Inverse Trig
Functions
d
u'
arcsin u  
dx
1 u2
d
u'
arctan u   2
dx
1 u
d
u'
arc sec u  
dx
u u 2 1
d
 u'
arccos u  
dx
1 u2
d
 u'
arc cot u   2
dx
1 u
d
 u'
ar csc u  
2
dx
u u 1
Examples:
1) Find an equation of the tangent line to the
graph at the indicated point.
f ( x)  arctan x
2) Find dy
dx
 

  1,

4 

a)
y  (arcsin x)e x
b)
x
y  2 ln( x  4)  arctan
2
2
More Examples
1) Find the slope of the tangent line to the
graph of the equation at the given point.
arctan( xy)  arcsin( x  y )
0,0