   Chapter 2.3, Problem 17E

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# 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:  ddxxn=nxn-1

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

Then  ddxfx+gx=ddxfx+ddxg(x)

Given:

y=x2 +4x +3 x

Calculations:

y=x2 +4x +3 x

By using rule of exponents, y can be written as

y=x2 +4x +3x12

=x2x12+4xx12+3x12

=x2-12+4x1-12 +3x-12

=x32+4x12+3x-12 .

Differentiating with respect to x,

By using addition rule of differentiation,

ddxfx+ gx=ddxfx+ddxgx

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