   Chapter 9.6, Problem 44E ### 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

# Stimulus-response The relation between the magnitude of a sensation y and the magnitude of the stimulus x is given by y = k ( x   —   x 0 ) n where k is a constant, x 0 is the threshold of effective stimulus, and n depends on the type of stimulus. Find the rate of change of sensation with respect to the amount of stimulus for each of Problems 42-44.For the stimulus of visual brightness y = k ( x − x 0 ) 1 / 3

To determine

To calculate: The rate of change of sensation with respect to the amount of stimulus of visual brightness y=k(xx0)1/3, where k is a constant, x0 is the threshold of effective stimulus.

Explanation

Given Information:

The provided function is y=k(xx0)1/3.

Formula used:

The power rule of differentiation,

ddxxn=nxn1

Calculation:

Consider the provided function,

y=k(xx0)1/3

Consider (xx0) to be u,

y=ku1/3

Differentiate both sides with respect to x,

dydx=ddx(ku1/3)

Simplify using the power rule,

dydx=k13u131dudx=k3u2/3dudx

Substitute (xx0)

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