Chapter 2.3, Problem 17E

### Calculus (MindTap Course List)

8th Edition
James Stewart
ISBN: 9781285740621

Chapter
Section

### Calculus (MindTap Course List)

8th Edition
James Stewart
ISBN: 9781285740621
Textbook Problem
264 views

# Differentiate the function. y = x 2 + 4 x + 3 x

To determine

To differentiate:

y=x2 +4x +3 x

Explanation

Concept:

To differentiate given function, use rules of differentiation and also convert radicals into exponent form if necessary.

Formula:

(i) Power rule:Â  ddxxn=nxn-1

(ii) The addition rule, if fÂ  and g are both differentiable,

ThenÂ  ddxfx+gx=ddxfx+ddxg(x)

Given:

y=x2Â +4xÂ +3Â x

Calculations:

y=x2Â +4xÂ +3Â x

By using rule of exponents, y can be written as

y=x2Â +4xÂ +3x12

Â Â Â =x2x12+4xx12+3x12

=x2-12+4x1-12Â +3x-12

=x32+4x12+3x-12Â .

Differentiating with respect to x,

By using addition rule of differentiation,

ddxfx+Â gx=ddxfx+ddxgx

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