   Chapter 2.3, Problem 25E

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# Differentiate. f ( x ) = ( 5 x 2 − 2 ) ( x 3 + 3 x )

To determine

To differentiate: fx=(5x2-2)(x3+3x)

Explanation

1) Concept: To differentiate the given function, use rule of differentiation.

2) Formula:

i. Difference rule: ddxfx-gx=ddxfx-ddx(gx)

ii. Sum rule: ddxfx+gx=ddxfx+ddx(gx)

iii. Constant multiple rule: ddxCfx=Cddxfx, C is constant

iv. Power function rule: ddxxn=nxn-1

3) Given: fx=(5x2-2)(x3+3x)

4) Calculations:

fx=(5x2-2)(x3+3x)

By multiplying brackets

fx=5x5+15x3

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