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Find the derivative. Simplify where possible.$ y = sech x (1 + \ln sech x) $

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01:02

Amrita Bhasin

07:09

Mutahar Mehkri

Calculus 1 / AB

Chapter 3

Differentiation Rules

Section 11

Hyperbolic Functions

Derivatives

Differentiation

Sivadas P.

January 12, 2021

In coshx -1/2tanh^2 x.dx

Missouri State University

Campbell University

University of Michigan - Ann Arbor

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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Hello. Uh we have a problem number when we have the problem in which I'm going to find derivative of who I call to sake X one plus Ellen sake of hyperbolic function X. Okay. And so to find the web adi X. So we have to use the caution from under product rule keep first differentiate second. So zero place one by Sake X in two. This differentiation of sake access sake x. and uh 10 x. Okay minus six X. And the next all things that are hyperbolic minus ckx into dan X bless one plus Ellen six X minus sick X 10 X. So this will be canceled out. Basically we'll be left with sake X and minus dan X. Okay bless if you just open it up it will be yeah. Right okay. Let us write minus sake X then X minus alan seek X and two say tex 10 X. Okay So this will be -2 sake X. 10 X. And this will become simply minus and then say X sake X into 10 X. If you take sake X and 10 access common will be left with uh with negative side of course two plus Ln psychics they should be answered. Thank you. Every function is going to have a really function. Thank you so much.

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