Find d y / d x y=sinh(4 x-8)

Name: Problem 9, Chapter 6: Calculus Early Transcendentals
Uploaded: 2021-02-25T05:46:48-08:00
Duration: 56 s
Channel: Bobby Barnes
Description: Find d y / d x y=sinh(4 x-8)

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Key Concepts

Hyperbolic Functions

Hyperbolic functions are analogs of trigonometric functions but are defined using exponential functions. They include functions like sinh and cosh, which have applications in various areas such as calculus, physics, and engineering.

Chain Rule

The chain rule is a fundamental principle in calculus used to differentiate composite functions. It states that the derivative of a composite function is the derivative of the outer function evaluated at the inner function multiplied by the derivative of the inner function.

Differentiation of Hyperbolic Sine

The differentiation of the hyperbolic sine function, sinh(x), is based on its derivative, which is cosh(x). When applied to a composite function involving sinh, such as sinh(g(x)), the chain rule dictates that the derivative is cosh(g(x)) times the derivative of g(x).

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