Question

find $D_{x} y$. $$y=\sinh x \cosh 4 x$$

Name: Problem 24, Chapter 6: Calculus
Uploaded: 2021-06-17T05:03:31-08:00
Duration: 1 min 2 s
Channel: Tyler Moulton
Description: find Dx y. y=sinhx cosh4 x

   find $D_{x} y$.
$$y=\sinh x \cosh 4 x$$

Calculus

Dale Varberg, Edwin… 9th Edition

Chapter 6, Problem 24

Instant Answer

Solved by Expert Tyler Moulton

06/17/2021

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We need to find the derivative of this function with respect to $x$. Show more…

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find $D_{x} y$. $$y=\sinh x \cosh 4 x$$

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Key Concepts

Product Rule

The product rule is a fundamental concept in differential calculus used to differentiate a product of two functions. It states that the derivative of a product is the derivative of the first function times the second function, plus the first function times the derivative of the second. This rule allows us to find the derivative of complex functions by breaking them down into parts that can be differentiated individually.

Derivatives of Hyperbolic Functions

Derivatives of hyperbolic functions are essential in calculus, particularly when working with functions such as sinh(x) and cosh(x). The derivative of sinh(x) is cosh(x) and the derivative of cosh(x) is sinh(x). This knowledge is crucial for differentiating expressions involving hyperbolic functions, and it parallels the relationship between the trigonometric functions sin(x) and cos(x).

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