   Chapter 11.1, Problem 24E ### 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 d y d x  if y =ln  [ x 2 ( x 4 − x + 1 ) ] .

To determine

To calculate: The value of dydx for the function y=ln[x2(x4x+1)].

Explanation

Given Information:

The provided function is y=ln[x2(x4x+1)].

Formula Used:

The product rule for any positive numbers M and N, lnMN=lnM+lnN.

Derivative of natural logarithmic functions is such that, if y=lnu, where u is a differentiable function of x then dydx=1ududx.

Power of x rule for a real number n is such that, if f(x)=xn then f(x)=nxn1.

Constant function rule for a constant c is such that, if f(x)=c then f(x)=0.

Calculation:

Consider the function, y=ln[x2(x4x+1)]

Use product rule for logarithms,

y=lnx2+ln(x4x+1)

Differentiate with respect to x,

dydx=ddx[lnx2+ln(x4x+1)]=ddx(lnx2

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