10–19. Derivatives Find the derivatives of the following functions.
f(x) = (sinh x) / (1 + sinh x)

Find the derivative of the inverse of the following functions. Express the result with x as the independent variable.

f(x) = x^-1/3

Which of the following is the correct derivative of $y=arcsin\left(x\right)$ with respect to $x$?

10–19. Derivatives Find the derivatives of the following functions.

f(t) = cosh t sinh t

10–19. Derivatives Find the derivatives of the following functions.

f(x) = tanh⁻¹(cos x)

10–19. Derivatives Find the derivatives of the following functions.

g(t) = sinh⁻¹(√t)

Derivatives of hyperbolic functions Compute the following derivatives.

b. d/dx (x sech x)

Critical points Find the critical points of the function ƒ(x) = sinh² x cosh x.

88–91. Limits Use l’Hôpital’s Rule to evaluate the following limits.

lim x → ∞ (1 − coth x) / (1 − tanh x)