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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)=x2-x3+5x9x-1

Short Answer

Expert verified

The required answer is2x-32x12+45x8x-1+x2-x3+5x912x-32x-1

Step by step solution

01

Step 1. Given Information   

The given function isf(x)=x2-x3+5x9x-1

02

Step 2. Calculation    

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

f'(x)=ddxx2-x3+5x9x-1-x2-x3+5x9ddxx-1x-12=2x-32x32-1+5(9x8)x-1-x2-x3+5x9-12x-12-1x-1=2x-32x12+45x8x-1-x2-x3+5x9-12x-32x-1=2x-32x12+45x8x-1+x2-x3+5x912x-32x-1

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