Section 3.5 : Derivatives of Trig Functions
6. Differentiate \(f\left( w \right) = \tan \left( w \right)\sec \left( w \right)\) .
Show SolutionNot much to do here other than take the derivative, which will require the product rule.
\[f'\left( w \right) = \left[ {{{\sec }^2}\left( w \right)} \right]\sec \left( w \right) + \tan \left( w \right)\left[ {\sec \left( w \right)\tan \left( w \right)} \right] = \require{bbox} \bbox[2pt,border:1px solid black]{{{{\sec }^3}\left( w \right) + \sec \left( w \right){{\tan }^2}\left( w \right)}}\]