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Calculate each of the derivatives or derivative values in Exercises 47–52.

ddxx2+1x2+43x-2x=-1

Short Answer

Expert verified

ddxx2+1x2+43x-2x=-1is-24625

Step by step solution

01

Step 1. Given Information

We need to find ddxx2+1x2+43x-2x=-1

Let us writey=x2+1x2+43x-2

02

Step 2. Finding First Derivative

dydx=x2+43x-2ddxx2+1-x2+1ddxx2+43x-2x2+43x-22dydx=x2+43x-22x-x2+12x3x-2+x2+43x2+423x-22dydx=x2+46x2-4x-x2+16x2-4x+3x2+12x2+423x-22dydx=x2+46x2-4x-x2+19x2-4x+12x2+423x-22=-3x4+3x2+12x-12x2+423x-22

03

Step 3. Finding derivative at x=-1

dydx=-3-14+3-12+12-1-121+42-3-22dydx=-3+3-12-121+42-3-22=-24625

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