Chapter 9.5, Problem 52E

### Mathematical Applications for the ...

12th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781337625340

Chapter
Section

### Mathematical Applications for the ...

12th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781337625340
Textbook Problem

# Response to injected adrenalin Experimental evidence has shown that the response y of a muscle is related to the concentration of injected adrenaline x according to the equation y = x a + b x where a and b are constants. Find the rate of change of response with respect to the concentration.

To determine

To calculate: The rate of change of response with respect to the concentrations if the response y of a muscle is related to the concentration of injected adrenaline x is given by y=xa+bx.

Explanation

Given Information:

The response y of a muscle is related to the concentration of injected adrenaline x by y=xa+bx.

Formula Used:

The quotient rule for the derivative of the two function, ddx(fg)=gâ‹…dfdxâˆ’fâ‹…dgdxg2.

The sum and difference rule of derivate of functions, ddx[u(x)Â±v(x)]=ddxu(x)Â±ddxv(x).

The simple power rule of derivative ddx(xn)=nxnâˆ’1.

Calculation:

Consider the provided response y of a muscle and the concentration of injected adrenaline x related to each other by y=xa+bx.

Differentiate the provided population growth function,

dydx=ddx[xa+bx]

Use the quotient rule for the derivative of the two function f(x) and g(x) is, ddx(fg)=gâ‹…dfdxâˆ’fâ‹…dgdxg2

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