How Do I Solve 1st and 2nd Derivative Homework Problems?

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LiHJ
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Homework Statement



Dear Mentors PF Helpers,

Here's my question:

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I see it from my textbook with it solutions copied down below. Wonder is there another way to do it.
Thank you for your time.

Homework Equations



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The Attempt at a Solution


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Sorry forgot to copied these as well

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I do not see any other way than doing the differentiation. You may replace sec(x) by 1/cos(x), and replace the argument of the logarithm by (1+sinx)/cos(x) before differentiating.