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Section 3.8 : Derivatives of Hyperbolic Functions

For each of the following problems differentiate the given function.

1. \(h\left( w \right) = {w^2} - 3\sinh \left( w \right)\)
2. \(g\left( x \right) = \cos \left( x \right) + \cosh \left( x \right)\)
3. \(H\left( t \right) = 3{\mathop{\rm csch}\nolimits} \left( t \right) + 7\sinh \left( t \right)\)
4. \(A\left( r \right) = \tan \left( r \right)\tanh \left( r \right)\)
5. \(f\left( x \right) = {{\bf{e}}^x}\cosh \left( x \right)\)
6. \(\displaystyle f\left( z \right) = \frac{{{\mathop{\rm sech}\nolimits} \left( z \right) + 1}}{{1 - z}}\)
7. \(\displaystyle Q\left( w \right) = \frac{{\coth \left( w \right)}}{{w + \sinh \left( w \right)}}\)