   Chapter 11, Problem 8RE ### 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 1-12, find the derivative of each function. w = ( t 2 + 1 )  ln  ( t 2 + 1 ) − t 2

To determine

To calculate: The derivative of the provided function w=(t2+1)ln(t2+1)t2.

Explanation

Given Information:

The provided function is:

w=(t2+1)ln(t2+1)t2

Formula used:

The derivatives of logarithmic function:

ddxln(f(x))=1f(x)ddxf(x)

Where f(x) is a differentiable function of x.

The product rule of derivative:

ddx(uv)=udvdx+vdudx

Calculation:

Consider the provided function:

w=(t2+1)ln(t2+1)t2

Differentiate both sides with respect to t as:

dwdt=ddt[(t2+1)ln(t2+1)t2]

Now, use the product rule of derivative:

ddx(uv)

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