Thread: inverse derivs...

Consider the function below where x > 0.



(a) Find and simplify f '(x).

I need a little help with these bad johnnys...can someone show me how to do them, prefferably the steps...many thanks...

mathaction

Are you serious about needing help on g(x)? Take a good close look at it. You'll kick yourself.

These are just Chain Rule exercises.

For the first, you need to know these derivatives:







Show us what you get.

Originally Posted by TKHunny

Are you serious about needing help on g(x)? Take a good close look at it. You'll kick yourself.

These are just Chain Rule exercises.

For the first, you need to know these derivatives:







Show us what you get.

yeah i already did the g(x), its just pi because sin and arcsin cancel out and the derivative of pi(x) is just pi cause pi is constant and d/dx is just 1

d/dx(1/t) is 1/t^2, d/dx(arctan(t) is 1/(1+t^2), and d/dx(3t) is 3...now what do i do from here...

Hello, mathaction!

I must assume you know the derivative of the arctangent.

. .

We have: .

Chain Rule: .

We have: .

Therefore: .

This one has a surprising answer . . .

We have: .

. .


~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~


How come it works out to zero?

Let
Then: .

is in a right triangle with:
Here is the triangle:

Code:

                        *
                     *  *
                  *     *
               *        * x
            *           *
         * α            *
      * * * * * * * * * *
                1

Let
Then: .
is in a right triangle with:
Here is the triangle:

Code:

                        *
                     * β*
                  *     *
               *        * x
            *           *
         *              *
      * * * * * * * * * *
                1

Get it?
and are in the same right triangle.
They are complementary: .

We just differentiated a constant function: .