Transcript 3.8 Derivatives of Inverse Functions Mon Nov 19
3.8 Derivatives of Inverse Functions Mon Oct 27 Do Now Find the inverse of each function 1) Y = 3x - 5 2) Y = x^4 + 10
HW Review: p.175 #1-85
Derivative of the Inverse • Assume f(x) is differentiable and
g
(
x
) =
f
1 (
x
) • And if f’(g(x)) is not 0 then
g
'(
x
) = 1
f
'(
g
(
x
))
Inverse Derivatives • We can use the previous theorem to find the derivative of an inverse • We can also find the inverse first and differentiate directly
Ex 2 • Calculate g’(1) where g(x) is the inverse of f(x) = x + e^x
Inverse Trig Derivatives • One of these six might appear on the
d dx
AP exam:
d dx d dx
sec sin 1 tan 1
x
-
x
= 1 = 1 1 -
x
2
x
=
x
2 1
x x
2 1 + 1 1
d dx d dx
cos 1
x d dx
cot 1
x
csc 1
x
= = = 1
x
2 1 1 + 1 1
x
2
x x
2 1
Closure • Calculate
d dx
csc 1 (
e x
+ 1) where x = 0
DO NOW • Find the derivative 2
e
sin 4 (
x
3 -
x
) -
x
2 tan
x