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Find the derivatives of the functions in Exercises 21–46. Keep in mind that it may be convenient to do some preliminary algebra before differentiating.

f(x)=x(3x2+1)9

Short Answer

Expert verified

The required answer is(3x2+1)9+54x2(3x2+1)8

Step by step solution

01

Step 1. Given Information 

The given function isf(x)=x(3x2+1)9

02

Step 2. Calculation 

Differentiate both the sides with respect to x, we get,

f'(x)=ddx(x)(3x2+1)9+xddx(3x2+1)9=(3x2+1)9+x9(3x2+1)9-1ddx(3x2+1)=(3x2+1)9+x9(3x2+1)8ddx3x2+ddx1=(3x2+1)9+x9(3x2+1)83(2x)=(3x2+1)9+54x2(3x2+1)8

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