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Prove the identity.$ (\cosh x + \sinh x)^n = \cosh nx + \sinh nx $ ($ n $ any real number)

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Calculus 1 / AB

Chapter 3

Differentiation Rules

Section 11

Hyperbolic Functions

Derivatives

Differentiation

Harvey Mudd College

Baylor University

University of Michigan - Ann Arbor

Boston College

Lectures

04:40

In mathematics, a derivative is a measure of how a function changes as its input changes. Loosely speaking, a derivative can be thought of as how much one quantity is changing in response to changes in some other quantity; for example, the derivative of the position of a moving object with respect to time is the object's velocity. The concept of a derivative developed as a way to measure the steepness of a curve; the concept was ultimately generalized and now "derivative" is often used to refer to the relationship between two variables, independent and dependent, and to various related notions, such as the differential.

44:57

In mathematics, a differentiation rule is a rule for computing the derivative of a function in one variable. Many differentiation rules can be expressed as a product rule.

02:45

Prove the identity.

03:28

Prove that : ( cosh x - si…

00:36

Prove the identity.$ \…

01:04

Prove the identity.$$<…

00:28

01:07

Okay e to the x plus e to the negative x over 2 plus e to the s e to the negative x over 2 to the power of n we're just using the identity list. In the text book to the power of n choose cancel. We get e to the x to the power of n, which is e to the n x o. Now we have e to the n x times. 2. Over 2 gives us 2 e to the n x over 2, which we can now write as e to the n x plus e to the negative x over 2 plus e to the x minus e to the negative x over 2 point this equivalent to cosine X plus sine h, n x,

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