we can find the inverse function as follows: switch x and y. at x = 2 : to find the derivative of...
TRANSCRIPT
![Page 1: We can find the inverse function as follows: Switch x and y. At x = 2 : To find the derivative of the inverse function:](https://reader036.vdocuments.site/reader036/viewer/2022070412/56649e8f5503460f94b93d2c/html5/thumbnails/1.jpg)
We can find the inverse function as follows:
Switch x and y.
At x = 2:
To find the derivative of the inverse function:
![Page 2: We can find the inverse function as follows: Switch x and y. At x = 2 : To find the derivative of the inverse function:](https://reader036.vdocuments.site/reader036/viewer/2022070412/56649e8f5503460f94b93d2c/html5/thumbnails/2.jpg)
At x = 2:
At x = 4:
Slopes are reciprocals.
![Page 3: We can find the inverse function as follows: Switch x and y. At x = 2 : To find the derivative of the inverse function:](https://reader036.vdocuments.site/reader036/viewer/2022070412/56649e8f5503460f94b93d2c/html5/thumbnails/3.jpg)
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
![Page 4: We can find the inverse function as follows: Switch x and y. At x = 2 : To find the derivative of the inverse function:](https://reader036.vdocuments.site/reader036/viewer/2022070412/56649e8f5503460f94b93d2c/html5/thumbnails/4.jpg)
A typical problem using this formula might look like this:
Given:
Find:
Derivative Formula for Inverses:
![Page 5: We can find the inverse function as follows: Switch x and y. At x = 2 : To find the derivative of the inverse function:](https://reader036.vdocuments.site/reader036/viewer/2022070412/56649e8f5503460f94b93d2c/html5/thumbnails/5.jpg)
We can use implicit differentiation to find:
![Page 6: We can find the inverse function as follows: Switch x and y. At x = 2 : To find the derivative of the inverse function:](https://reader036.vdocuments.site/reader036/viewer/2022070412/56649e8f5503460f94b93d2c/html5/thumbnails/6.jpg)
We can use implicit differentiation to find:
But
so is positive.
![Page 7: We can find the inverse function as follows: Switch x and y. At x = 2 : To find the derivative of the inverse function:](https://reader036.vdocuments.site/reader036/viewer/2022070412/56649e8f5503460f94b93d2c/html5/thumbnails/7.jpg)
We could use the same technique to find and
.1sec
dx
dx-
![Page 8: We can find the inverse function as follows: Switch x and y. At x = 2 : To find the derivative of the inverse function:](https://reader036.vdocuments.site/reader036/viewer/2022070412/56649e8f5503460f94b93d2c/html5/thumbnails/8.jpg)
Your calculator contains all six inverse trig functions.However it is occasionally still useful to know the following:
p