   Chapter 11.1, Problem 34E ### 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

# In Problems 25-38, find y'. y = ln ( 3 x + 1 )

To determine

To calculate: The value of y for the function y=ln(3x+1).

Explanation

Given Information:

The provided function is y=ln(3x+1).

Formula Used:

Chain rule for function f(x)=u(v(x)) is f(x)=u(v(x))v(x).

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

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

Calculation:

Consider the function, y=ln(3x+1).

Rearrange the function,

y=[ln(3x+1)]1/2

Differentiate with respect to x,

dydx=ddx[ln(3x+1)]1/

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