Chapter 2: Q. 49 (page 210)

Calculate each of the derivatives or derivative values in Exercises 47–52.
${\frac{d^{2}}{d x^{2}} (\frac{3}{x^{- \frac{3}{2}} \sqrt{x}})}_{x = 2}$

Short Answer

Expert verified

${\frac{d^{2}}{d x^{2}} (\frac{3}{x^{- \frac{3}{2}} \sqrt{x}})}_{x = 2} = 0$

Step by step solution

Step 1. Given Information

We need to find the second order derivative of ${\frac{d^{2}}{d x^{2}} (\frac{3}{x^{- \frac{3}{2}} \sqrt{x}})}_{x = 2}$

Let us write $y = (\frac{3}{x^{- \frac{3}{2}} \sqrt{x}}) = \frac{3}{x^{\frac{- 3}{2} + \frac{1}{2}}} = \frac{3}{x^{- 1}} = 3 x$

Step 2. Finding First order derivative

$\frac{d y}{d x} = 3$

Step 3. Finding second order derivative

$\frac{d^{2} y}{d x^{2}} = 0$

at $x = 2$ , ${\frac{d^{2}}{d x^{2}} (\frac{3}{x^{- \frac{3}{2}} \sqrt{x}})}_{x = 2}$ is zero.

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Calculate each of the derivatives or derivative values in Exercises 47–52.
${\frac{d^{2}}{d x^{2}} (\frac{3}{x^{- \frac{3}{2}} \sqrt{x}})}_{x = 2}$

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Finding First order derivative

Step 3. Finding second order derivative

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Calculate each of the derivatives or derivative values in Exercises 47–52.d2dx23x-32xx=2

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Finding First order derivative

Step 3. Finding second order derivative

One App. One Place for Learning.

Most popular questions from this chapter

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Mechanics Maths

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Theoretical and Mathematical Physics

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Study anywhere. Anytime. Across all devices.

Calculate each of the derivatives or derivative values in Exercises 47–52.
${\frac{d^{2}}{d x^{2}} (\frac{3}{x^{- \frac{3}{2}} \sqrt{x}})}_{x = 2}$