Question

Differentiate. $$y=\frac{e^{x}-1}{e^{x}+1}$$

Name: Problem 17, Chapter 7: Calculus: One Variable
Uploaded: 2021-07-26T18:13:41-08:00
Duration: 1 min 32 s
Channel: Edward Downes
Description: Differentiate. y=(e^x-1)/(e^x+1)

   Differentiate.
$$y=\frac{e^{x}-1}{e^{x}+1}$$

Calculus: One Variable

Garret J. Etgen,… 10th Edition

Chapter 7, Problem 17

Instant Answer

Solved by Expert Edward Downes

07/26/2021

Step 1

Step 1: We start by applying the quotient rule for differentiation which states that the derivative of a quotient of two functions is given by: \[ \frac{d}{dx}\left(\frac{u}{v}\right) = \frac{vu' - uv'}{v^2} \] where $u = e^x - 1$ and $v = e^x + 1$. Show more…

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Differentiate. $$y=\frac{e^{x}-1}{e^{x}+1}$$

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Key Concepts

Differentiation

Differentiation is a fundamental concept in calculus that involves finding the derivative of a function, which represents the rate at which the function's value changes with respect to changes in its input.

Quotient Rule

The quotient rule is a method used to differentiate functions that are expressed as the ratio of two differentiable functions. It states that the derivative of a quotient f(x)/g(x) is given by (f'(x)g(x) - f(x)g'(x)) divided by g(x)².

Exponential Functions

Exponential functions, particularly those expressed as e^x, have the unique property that their rate of change (derivative) is equal to the function itself. This property simplifies the process of differentiation when exponential terms are involved.

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