We can find the inverse function as follows: Switch x and y. At x = 2 : To find the derivative of...
-
Upload
stanley-simmons -
Category
Documents
-
view
215 -
download
0
Transcript of We can find the inverse function as follows: Switch x and y. At x = 2 : To find the derivative of...
We can find the inverse function as follows:
Switch x and y.
At x = 2:
To find the derivative of the inverse function:
At x = 2:
At x = 4:
Slopes are reciprocals.
Slopes are reciprocals.
Because x and y are reversed to find the reciprocal function, the following pattern always holds:
Derivative Formula for Inverses:evaluated at
is equal to the reciprocal of
the derivative of
evaluated at .
The derivative of
A typical problem using this formula might look like this:
Given:
Find:
Derivative Formula for Inverses:
We can use implicit differentiation to find:
We can use implicit differentiation to find:
But
so is positive.
We could use the same technique to find and
.1sec
dx
dx-
Your calculator contains all six inverse trig functions.However it is occasionally still useful to know the following:
p