Differentiate polar curve

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I have attempted this question but have not found a solution. I am currently stuck. Hints on how I may go further would be helpful. Thank You in advance.

The Question: enter image description here

What I have done so far: enter image description here

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What you're doing is correct and is the same way I would have done it. Once I read Claude Leibovici's comments I figured the problem is with the book.