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Find the differential of each of the given functions.$$y=2 \sqrt{x}-\frac{1}{8 x}$$

$d y=\left(\frac{1}{\sqrt{x}}+\frac{1}{8 x^{2}}\right) d x$

Calculus 1 / AB

Chapter 24

Applications of the Derivative

Section 8

Differentials and Linear Approximations

Derivatives

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Lectures

03:09

In mathematics, precalculu…

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In mathematics, a function…

01:38

Find the differential of e…

05:21

Solve the given differenti…

01:09

Find the differential of t…

02:51

11:49

00:24

Verify that the given func…

05:02

02:31

Use the differential $d y$…

03:44

Find the general solution …

01:21

$1-8$ " Solve the dif…

okay. Part A The derivative using the product rule. We have acts times You did the negative for ox Natural order of E. We know that we're taking the derivative of negative four acts. So in this case, this simplifies to negative for X E to the negative or ax plus e to the night of four ax using the chain rule and factoring we end up with Okay, Part B. We know that we have one nice t to the fourth to the 1/2. Therefore we have, if you have tea, is one nice to the fourth than we know that we could have 1/2 you to the negative. 1/2 comes negative for t cubed, which is negative to t cubed over the square root of one minus t to the fourth.

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