   Chapter 11.3, Problem 17E Finite Mathematics and Applied Cal...

7th Edition
Stefan Waner + 1 other
ISBN: 9781337274203

Solutions

Chapter
Section Finite Mathematics and Applied Cal...

7th Edition
Stefan Waner + 1 other
ISBN: 9781337274203
Textbook Problem

In Exercises 13-28, calculate d y d x . Simplify your answer. [HINT: See Example 1 and 2.] y = ( 2 x + 3 ) 2

To determine

To calculate: The derivative of function y=(2x+3)2.

Explanation

Given Information:

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

Formula used:

Product rule of derivative of differentiable functions, f(x) and g(x) is,

ddx[f(x)g(x)]=f'(x)g(x)+f(x)g'(x)

Sum rule of derivative is ddx[f(x)+g(x)]=ddxf(x)+ddxg(x).

Derivative of function y=xn using power rule is ddx(xn)=nxn1.

Derivative of a constant is 0.

Calculation:

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

Rewrite the function as the product of two binomials,

y=(2x+3)2=(2x+3)(2x+3)

Apply product rule of derivative,

dydx=ddx(2x+3)(

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