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7) y = In (sinh 9x) 7) A) 9 csch 9x B) 9 coth 9x C) - D) coth 9x sinh 9x Find the derivative of y with respect to the appropriate variable. 8) y = sinh-1 19x 8 ) A) - 219x(1 + 9x) B) - 219x(1 + 9x) C) JI + 9x D) 29x(9x - 1) 9 ) y = (02 +50) tanh-1 (0 + 4) 9 ) A) (20 + 5) tanh -1 (0 + 4) - 02 + 50 1 + (0+4)2 B) (20 + 5) tanh-1 (0+ 4) - - 0 + 3 C) - T e 1 0 + 3 D) (20+5) . 0 + 15 10) y = 9 tanh- (cos x) 10) A) In- 1 sin x B) V1 -x2 sin x C) - -9 sin x D) 1+ cos2 x cos x 11) Verify the identity using the definitions of hyperbolic functions. 11) coth x = - e 2x + 1 e2x - 1 12) Use the fundamental identity cosh2 x - sinh2 x = 1 to verify the identity. 12 ) 1 - tanh2 x = sech2 x 13) Derive the formula given that d/dx (cosh x) = sinh x and d/dx (sinh x) = 13 ) cosh x. d/dx (coth x) = -csch2 x