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Section 3.7 : Derivatives of Inverse Trig Functions

For each of the following problems differentiate the given function.

1. \(f\left( x \right) = \sin \left( x \right) + 9{\sin ^{ - 1}}\left( x \right)\)
2. \(C\left( t \right) = 5{\sin ^{ - 1}}\left( t \right) - {\cos ^{ - 1}}\left( t \right)\)
3. \(g\left( z \right) = {\tan ^{ - 1}}\left( z \right) + 4{\cos ^{ - 1}}\left( z \right)\)
4. \(h\left( t \right) = {\sec ^{ - 1}}\left( t \right) - {t^3}{\cos ^{ - 1}}\left( t \right)\)
5. \(f\left( w \right) = \left( {w - {w^2}} \right){\sin ^{ - 1}}\left( w \right)\)
6. \(y = \left( {x - {{\cot }^{ - 1}}\left( x \right)} \right)\left( {1 + {{\csc }^{ - 1}}\left( x \right)} \right)\)
7. \(\displaystyle Q\left( z \right) = \frac{{z + 1}}{{{{\tan }^{ - 1}}\left( z \right)}}\)
8. \(\displaystyle A\left( t \right) = \frac{{1 + {{\sin }^{ - 1}}\left( t \right)}}{{1 - {{\cos }^{ - 1}}\left( t \right)}}\)