   Chapter 2.3, Problem 26E

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# Differentiate. B ( u ) = ( u 3 + 1 ) ( 2 u 2 − 4 u − 1 )

To determine

To differentiate:

Bu=(u3+1)(2u2-4u-1)

Explanation

1) Concept: To differentiate the given function, Use rules of differentiability.

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: Bu=(u3+1)(2u2-4u-1)

4) Calculations:

Bu=(u3+1)(2u2-4u-1)

By solving brackets

Bu=2u5-4u4-u3+2u2-4u-1

Now differentiate B(u) with respect to u

B'(u)=ddu2u5-4u4

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