(problem 83) any would be appreciated : ) i have the answer key, i just don't know how to get the answer, so explaining each step would be great!

To find the derivative of this function, there is a property that we should know called the Constant Multiple Rule, which says:

(where is a constant)

Remember that the derivative of is . However, you may notice that we are finding the derivative of , not . So, we are going to have to use the chain rule. To complete the chain rule for the derivative of a trigonometric function (in layman's terms) is basically the following: First, complete the derivative of the trig function as you would if what was inside the trig function is . Then, take the derivative of what's inside of the trig function and multiply it by what you found in the first step.

Let's apply that to our problem. Right now, I am not going to worry about the at the front of the equation, since we can just multiply it back in at the end of our problem. So, let's examine . We see that what's inside the trig function is , which has a derivative of 2. Thus, let's first find the derivative of as if was just and then multiply it by 2.

The derivative of would first be . Multiplying it by 2, we get our derivative of . However, don't forget to multiply it by the that we removed near the beginning. This gives us our final derivative of .

Remember that we now have to find the derivative at the given point. To do this, simply "plug in" the point into the derivative using the x-coordinate. This is shown below:

Our final answer is 0.

b mark me branliest thx

step-by-step explanation:

yes   because as the functions are graphed they eventually will intersect unless otherwise

step-by-step explanation: