SUMMARY
The derivative of the function y = sinh-1(1/x) can be found using implicit differentiation. Starting with the equation sinh(y) = 1/x, the differentiation process leads to the formula y' = -1/(cosh(y) * x2). To complete the solution, cosh(y) must be expressed in terms of x using hyperbolic identities. This approach simplifies the differentiation process and provides a clear path to the solution.
PREREQUISITES
- Understanding of hyperbolic functions, specifically sinh and cosh.
- Knowledge of implicit differentiation techniques.
- Familiarity with calculus concepts, particularly derivatives.
- Ability to manipulate algebraic expressions involving trigonometric identities.
NEXT STEPS
- Study hyperbolic function identities and their derivatives.
- Learn more about implicit differentiation methods in calculus.
- Explore examples of differentiating inverse hyperbolic functions.
- Practice expressing hyperbolic functions in terms of algebraic variables.
USEFUL FOR
Students studying calculus, particularly those focusing on differentiation techniques, as well as educators looking for examples of implicit differentiation involving hyperbolic functions.