Hi @Ammar_Jawed,
It seems to me your logic is that because the equations in the blue box appear the same as the derivatives for squared cost for linear regression, then it implies that those equations are not the derivatives for logistic cost for logistic regression.
That is not correct, because their derivatives do appear the same form, and you would have seen it if you had worked out the derivatives step by step yourself. Check out this post for the steps.
Raymond