1. 4-3 inviting inverses of trig deriv’s
Derivatives of inverse trig functions

2. Some things to note:
The inverse of a function can be found by reflecting
over the line y = x (interchanging the x & y)
If there is a tangent line at (a, f (a)), then the tangent
line at the inverse (f (a), a) has a slope that is the
reciprocal of the original tangent slope.
Original Inverse
(x, y) (y, x)
tangent slope
tangent slope

3. Thm: If f is differentiable at every point of an interval I,
and is never 0 on I, then f has an inverse and f –1 is
differentiable at every point of the interval f ( I ).
(Note: The derivatives of the inverse trig functions are found by doing implicit differentiation and using trig identities.)
Derivative of the Arcsine:

4. Derivative of the Arctangent:
Ex 2) A particle moves along the x-axis so that its position at any time t  0 is What is the velocity of the particle when t = 16?

5. Derivative of the Arcsecant:
Ex 3) Find

6. Remember:
Note: Derivatives of inverse cofunctions are the negatives of the derivatives of the corresponding inverse functions.
Derivatives of the Arccosine, Arccotangent and Arccosecant

7. Remember calculator conversions:
Ex 4) Find an equation for the tangent line to the graph
of y = cot –1 x at x = –1.
point
 m

8. homework
Pg #6 – 42 (mult of 6)
Pg #3 – 27 (mult of 3)