# Warmup: 1). 3.8: Derivatives of Inverse Trig Functions.

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Warmup: 1)

3.8: Derivatives of Inverse Trig Functions

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.

Because x and y are reversed to find the reciprocal function, the following pattern always holds: evaluated at is equal to the reciprocal of the derivative of evaluated at. The derivative of

The Rule for Inverses: Let f be a function that is differentiable on an interval. If f has an inverse function g, the g is differentiable at any x for which In other words if

A typical problem using this formula might look like this: ** if f(3)=5, then g(5)=3

since f(6) = 3,

Ans: Since we do not know g(5) which we need to remember that it is an inverse of f, so if g(5) = a, then f(a) = 5. set

We can use implicit differentiation to find:

But so is positive.

We could use the same technique to find and. 1 sec d x dx  Remember

the end

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