   Chapter 11.2, Problem 36E ### 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

# (a) What is the slope of the line tangent to y = e - x / ( 1 + e - x ) at x = 0 ? (b) Write the equation of the line tangent to the graph of y = e - x / ( 1 + e - x ) at x = 0.

(a)

To determine

To calculate: The slope of a line tangent to y=ex1+ex at x=0.

Explanation

Given Information:

Equation of the curve, y=ex1+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 product rule of differentiation:

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

Where u and v are differentiable functions of x.

The first derivative of curve y=f(x) describe the slope of tangent at point (x,y).

Calculation:

Consider the function provided,

y=ex1+ex

Now differentiate both sides with respect to x,

dydx=ddx(ex1+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(ex1+ex)=(1+ex)ddx(e

(b)

To determine

To calculate: The equation of a line tangent to the graph of y=ex1+ex at x=0.

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