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