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Prove the formulas given in Table 6 for the derivatives of the following functions.

(a) $ \cosh^{-1} $

(b) $ \tanh^{-1} $

(c) $ csch^{-1} $

(d) $ sech^{-1} $

(e) $ \coth^{-1} $

A. $\frac{1}{\sqrt{x^{2}-1}}$

B. $\frac{1}{1-x^{2}}$

C. $-\frac{1}{|x| \sqrt{x^{2}+1}}$

D. $-\frac{1}{x \sqrt{1-x^{2}}}$

E. $\frac{1}{1-x^{2}}$

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