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Find the derivative. Simplify where possible.$ y = x \sinh^{-1} (x/3) - \sqrt {9 + x^2} $

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Calculus 1 / AB

Chapter 3

Differentiation Rules

Section 11

Hyperbolic Functions

Derivatives

Differentiation

Campbell University

Harvey Mudd College

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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04:08

we know that we're looking at one over the squared of one plus U squared is the general formula we're plugging into. Therefore, why prime as Axe Times one over the spurt of one plus acts over three squared that's obviously export over nine times 1/3 plus sign h the minus one of X over three minus acts over the square root of nine plus X squared. This simplifies to sign a TSH to the negative one of X over three in other words, 1/3 x.

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