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

d2dx25x4-3x272x3+1

Short Answer

Expert verified

d2dx25x4-3x272x3+1=6x125x2-357750x7-5170x5+3150x4+816x3-1925x2+273

Step by step solution

01

Step 1. Given Information

We asks to find the second order derivative of d2dx25x4-3x272x3+1

Let us writey=5x4-3x272x3+1

02

Step 1. Finding First order derivative

dydx=2x3+1ddx5x4-3x27+5x4-3x27ddx2x3+1dydx=72x3+15x4-3x26ddx5x4-3x2+5x4-3x276x2dydx=2x135x2-36155x5-51x3+70x2-21

03

Step 3. Finding Second Order Derivative 

d2ydx2=5x2-36155x5-51x3+70x2-21ddx2x13+2x13155x5-51x3+70x2-21ddx5x2-36+2x135x2-36ddx155x5-51x3+70x2-21d2ydx2=26x125x2-36155x5-51x3+70x2-21+12x1310x-0155x5-51x3+70x2-21+2x135x2-36775x5-153x2+140x-0d2ydx2=6x125x2-357750x7-5170x5+3150x4+816x3-1925x2+273

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