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(a) Find the differential $ dy $ and (b) evaluate $ dy $ for the given values of $ x $ and $ dx. $$ y = \cos \pi x, x = \frac {1}{3}, dx = -0.02 $

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Calculus 1 / AB

Chapter 3

Differentiation Rules

Section 10

Linear Approximation and Differentials

Derivatives

Differentiation

Missouri State University

Campbell University

Oregon State University

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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$15-18$ (a) Find the diffe…

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Find the differential dy o…

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Find $dy/dx$ for the follo…

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Find dy/dx for the followi…

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$$ \begin{array}{l}{15-18 …

00:23

we know that after Texas coastline next there for of products is negative. Sign X Therefore of G of x is pi acts this part over here then g prime of X is pi therefore are y prime would be negative pi sign pi x Okay, Part B plug and negative pi sign high over three times negative 0.2 It's in the last 20.1 square root of three times pi.

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