`g(theta) = sec((1/2)theta)tan((1/2)theta)` Find the derivative of the function.

Textbook Question

Chapter 2, 2.4 - Problem 50 - Calculus of a Single Variable (10th Edition, Ron Larson).
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nees101 | Student, Graduate | (Level 2) Adjunct Educator

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Given the function `g(theta)=sec((theta)/2)tan((theta)/2)` . We have to find its derivative.

Here we will apply the product rule i.e.,

`d/(d theta)(uv)=uv'+u'v`

So here we have,

`d/(d theta)(sec(theta/2)tan(theta/2))=sec(theta/2)d/(d theta)(tan(theta/2))+d/(d theta)(sec(theta/2))tan(theta/2)`

                               `=sec(theta/2)[1/2sec^2(theta/2)]+[1/2sec(theta/2)tan(theta/2)]tan(theta/2)`

`1/2sec(theta/2)[sec^2(theta/2)+tan^2(theta/2)]`

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