   Chapter 11.1, Problem 26E ### 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 = x 2 ln ( 2 x + 3 )

To determine

To calculate: The value of y for the function y=x2ln(2x+3).

Explanation

Given Information:

The provided function is y=x2ln(2x+3).

Formula Used:

Product rule for function f(x)=u(x)v(x), where u and v are differentiable functions of x, then f(x)=u(x)v(x)+v(x)u(x).

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.

Calculation:

Consider the function, y=x2ln(2x+3)

Differentiate with respect to x,

dydx=ddx[x2ln(2x+3)]

Use the product rule of derivatives,

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