Line 2 to line 3, you need parentheses:

|ln(a·b)|c - ln(a·b)|

|:-|:-|

|ln(a)+ln(b)|c - (ln(a)+ln(b))|

Line 3 to line 4, you need the chain rule:

|f(x)|ln(x)|ln(7x)|ln(-x)

|:-|:-|:-|:-|

|f'(x)|1/x|7·(1/7x)|-1·(1/-x)|

Line 6 to line 7, you didn't change the numerator of the left fraction, you only multiplied the denominator