You aren't suppose to post lists of problems like this. It's againsts the rules of the forum. You should show some of your work so that we know what you're struggling with.

If you're in a calculus class, and you've been assigned these problems, then you should be familiar with the basic rules of differentiation. The functions you listed are all composite trig functions. This means that you need to use the chain rule, and the derivatives of the trig functions in their most basic forms. I'll help you get started with a few of them.

Problem 1

Think of it like this. Let .

Then

The derivative can be found by the chain rule.

See if you can finish this.

---------------------------------------------------------------

Problem 2

For a function like

Just apply an extended version of the chain rule.

Let

So you can write:

You still have a composite function here, so use another variable:

Let

Now just apply the chain rule.

See if you can finish.

---------------------------------------------------------------

Problems 5 and 6

For tangent lines, you should be familiar with the fact that the equation of the tangent line to the curve at the point is . This is a basic fact, and should be easy to apply to the functions you were given in problems 5 and 6.