Question: Hyperbolic Functions Certain combinations of the exponential functions e x and e x arise so frequently in mathematics and its applications that they deserve

Hyperbolic Functions

Certain combinations of the exponential functions e^x and e^−x arise so frequently in mathematics and its applications that they deserve to be given special names. This project explores the properties of functions called hyperbolic functions. The hyperbolic sine hyperbolic cosine, hyperbolic tangent, and hyperbolic secant functions are defined as follows:

sinh x= tinh rem 2 e sinh r cosh x cosh x

The reason for the names of these functions is that they are related to the hyperbola in much the same way that the trigonometric functions are related to the circle.

The differentiation formulas for the hyperbolic functions are analogous to those for the trigonometric functions, but the signs are sometimes different.

(a) Show that (b) Discover formulas for the derivatives of y = cosh x and y = tanh x. = sech x = et ti +e 2 cosh x

sinh x= tinh rem 2 e sinh r cosh x cosh x = sech x = et ti +e 2 cosh x

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