yes, method II is wrong, as you ended up with the wrong answer, but, in any case, you are making things wwaaayyyy too complicated.

recall that

where is a constant.

in other words, when finding the derivative of a function with a constant in front of it, we can simply find the derivative of the function without the constant, and then multiply it by the constant.

so,

the general rule: for some constant, so you could actually omit the second line altogether