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Find the numerical value of each expression.(a) $ sech 0 $ (b) $ \cosh^{-1} 1 $

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(a) $\operatorname{sech} 0=\frac{1}{\cosh 0}=\frac{1}{1}=1$(b) $\cosh ^{-1} 1=0$ because $\cosh 0=1$

Calculus 1 / AB

Chapter 3

Differentiation Rules

Section 11

Hyperbolic Functions

Derivatives

Differentiation

Oregon State University

Harvey Mudd College

University of Michigan - Ann Arbor

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.

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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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we know the form that we're gonna be using as to over eat of the exposed to the negative axe. Plug in zero. This is to over one plus one, which is to over two, which is one we know we're gonna have the natural log of acts, plus the square root of X squared minus one. This is the natural of one which you know is simply zero.

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