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Compute $ \Delta y $ and $ dy $ for the given values of $ x $ and $ dx = \Delta x. $ Then sketch a diagram like Figure 5 showing the line segments with lengths $ dx, dy, $ and $ \Delta y. $$ y = \sqrt {x -2}, x = 3, \Delta x = 0.8 $

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$d y=0.4$ and $\Delta y \approx 0.34$

Calculus 1 / AB

Chapter 3

Differentiation Rules

Section 10

Linear Approximation and Differentials

Derivatives

Differentiation

Baylor University

University of Michigan - Ann Arbor

Idaho State University

Lectures

04:40

In mathematics, a derivative is a measure of how a function changes as its input changes. Loosely speaking, a derivative can be thought of as how much one quantity is changing in response to changes in some other quantity; for example, the derivative of the position of a moving object with respect to time is the object's velocity. The concept of a derivative developed as a way to measure the steepness of a curve; the concept was ultimately generalized and now "derivative" is often used to refer to the relationship between two variables, independent and dependent, and to various related notions, such as the differential.

44:57

In mathematics, a differentiation rule is a rule for computing the derivative of a function in one variable. Many differentiation rules can be expressed as a product rule.

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$19-22$ Compute $\Delta y$…

Okay, take the derivative. Remember the chan. Roll off one g times G prime. You have one times one over to squirt of X minus two. Okay, this means we're derivative. Simply one over to scored of experts to This is times DX. Therefore, we know the change in X is on the top. We can plug in after three plus 0.8 minus off of three equals the skirt of 1.8 minus one with just 0.34 approximately. You know, this is do you? Why this area like this would be the change in axe.

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