Gradient Descent for logistic regression proof

Hello . I saw the gradient descent term for logistic regression , and I tried to derive the derivative term myself , but I think its quite different from whats shown in the course(ML specialization coursera) . Could anyone help ?
The first attached image is the actual term ,and sorry for the rough work , but in the second image the last line is what I came at .

submitted by /u/myvowndestiny to r/learnmachinelearning
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