(I attached my work as well as my answer guide)(Question #1 d)

When taking the derivative of a function, it is possible to obtain different algebraic formulas to the same function. I just wanted to know if my work is wrong or correct and if it is in fact equal to the answer or not. I don't want to go on assuming I am correct if I'm not which is why I'm asking for confirmation here.

Any input would be greatly appreciated!

Thanks in advance!