So the first thing to do is notice that this is a fraction and the quotient rule must be applied. The general form of the quotient rule is #d/dy[f(y)/g(y)] = (g(y)f'(y)-g'(y)f(y))/(g(y))^2#.
Time to assign #f(y)# and #g(y)# and calculate their derivatives #f'(y)# and #g'(y)#. The top function is our #f(y)# so #f(y)=7y+y^2# and #g(y)=y+1#. Their derivatives are #f'(y)=7+2y# and #g'(y)=1#. Now that we have each separate piece of the derivative, it's time to plug them into the whole.
#((1+y)(7+2y)-(7y+y^2)(1))/(1+y)^2#. Then you distribute the factors on top and combine like terms to get the answer above.
