Section 3.7 : Derivatives of Inverse Trig Functions
4. Differentiate \(f\left( w \right) = \sin \left( w \right) + {w^2}{\tan ^{ - 1}}\left( w \right)\) .
Show SolutionNot much to do here other than take the derivative using the formulas from class.
\[\require{bbox} \bbox[2pt,border:1px solid black]{{f'\left( w \right) = \cos \left( w \right) + 2w{{\tan }^{ - 1}}\left( w \right) + \frac{{{w^2}}}{{1 + {w^2}}}}}\]