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Differentiate.

$ y = \frac {\sqrt{x}}{2 + x} $

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00:27

Frank Lin

Calculus 1 / AB

Chapter 3

Differentiation Rules

Section 2

The Product and Quotient Rules

Derivatives

Differentiation

Missouri State University

Campbell University

Harvey Mudd College

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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Hey, it's Claire. So in your brain here, So we're gonna find the derivative and respect to X. We're a square root of X over X plus two. This becomes equal to D over DX for square root of X turned X plus two minus square root of X D over DX your X plus two all over X plus two square. I'm only simplify. We got X plus two over two square root of Epps, minus one plus zero square root of X over X plus two square. We're just equal to X plus two over two square root of X minus square root of X over X plus two squared just equal to negative X minus two over two square root of X times X plus two square.

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