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Prove Equation 5 using (a) the method of Example 3 and (b) Exercise 18 with $ x $ replaced by $ y. $

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Calculus 1 / AB

Chapter 3

Differentiation Rules

Section 11

Hyperbolic Functions

Derivatives

Differentiation

Baylor University

University of Nottingham

Boston 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.

00:26

In Exercises $15-20,$ solv…

01:43

For Exercises 5 and $6,$ c…

Okay. We know that X is either y minus C to the native. Lie over each of the y plus e to the negative. Why? Therefore, we have X minus one each of the two. Why is equivalent to negative one plus tax? Therefore, either too. Why one plus ax over one minus x the natural log of each of the two. Why the natural of one plus acts over one minus X? Because we're taking the nuptial both sides drink. This gives us why is 1/2 natural look of one plus acts for one minus X Therefore could just consider this to be inverse tangent Kovacs and we know that X is between negative one positive one.

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