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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
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