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(a) Find the differential $ dy $ and (b) evaluate $ dy $ for the given values of $ x $ and $ dx. $$ y = \sqrt {3 + x^2}, x = 1, dx = -0.1 $

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Calculus 1 / AB

Chapter 3

Differentiation Rules

Section 10

Linear Approximation and Differentials

Derivatives

Differentiation

Missouri State University

University of Michigan - Ann Arbor

University of Nottingham

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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(a) Find the differential …

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05:08

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02:20

Find the differential dy o…

02:30

, find dy/dx by logarithmi…

01:21

Compute $dy/dx$ for the fo…

02:08

okay, We know that we're gonna be doing 1/2 times three plus X squared to the night of 1/2. Remember, take into account the changeable times two acts. The derivative of the inside of X squared is to actually have to multiply that as well. This gives us acts over the square root of three plus X squared de axe. OK, moving on into part B, we can simply pull again. One over the square root of four terms. Negative 0.1 because negative 0.5

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