Deriving some inverse trig functions and some integrals

Hi all!

I am having some trouble with a few problems I've been working on.

Find the derivatives of the function

Step was was recognizing the product rule for

so I have

but I am not sure that it is right

Problem number two: Find the derivative of

this one threw me a monkey wrench right away since the argument to arccos is only x and not a function of x. even if it were more then just x i'm still scratching my head on how to start this one

Problem three:

Intergrate

I figured to used the identity that

So I then went to complete the square to give me what I wanted

I got

so then my denominator turned into 7 + (3x+1)^2 which I figured was wrong. A little confused on this one.

Same for this last problem

any help would be appreciated!!!