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Section 3.7 : Derivatives of Inverse Trig Functions

For each of the following problems differentiate the given function.

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