   Chapter 11.2, Problem 30E ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042

#### Solutions

Chapter
Section ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042
Textbook Problem

# Find the derivatives of the functions in Problems 1-34. y = e x − e − x e x + e − x

To determine

To calculate: The derivative of function, y=exexex+ex.

Explanation

Given Information:

The function provided is y=exexex+ex.

Formula used:

The quotient rule of differentiation:

ddx[u(x)v(x)]=v(x)ddxu(x)u(x)ddxv(x)[v(x)]2 [forv(x)0]

Where u and v are differentiable functions of x.

The differentiation of exponential function y=eu with respect to x:

ddxeu=eududx

Where u is a differentiable function of x.

Calculation:

Consider the provided function,

y=exexex+ex

Now differentiate both sides with respect to x,

dydx=ddx(exexex+ex)

Now apply, quotient rule of differentiation:

ddx[u(x)v(x)]=v(x)ddxu(x)u(x)ddxv(x)[v(x)]2

To obtain the derivative as:

ddx(exexex+ex)=(ex+ex)ddx(exex)(exex)ddx(ex

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