Problem

Find the derivative. Simplify where possible. $ …

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Problem 39 Hard Difficulty

Find the derivative. Simplify where possible.
$ g(t) = t \coth \sqrt {t^2 + 1} $

Answer

$g^{\prime}(t)=c$ oth $\sqrt{t^{2}+1}-\frac{t^{2}}{\sqrt{t^{2}+1}}\left(\operatorname{csch}^{2} \sqrt{t^{2}+1}\right)$

Topics

Derivatives

Differentiation

Book Cover for Calculus: Early Tra…

Calculus: Early Transcendentals

Chapter 3

Differentiation Rules

Section 11

Hyperbolic Functions

Discussion

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Video Transcript

Okay. We know that G Prime of tea. Using the product rule would be one times coach tangent h squared of t squared, plus one with tee times. This is a prevalent to co tangent H squirt of cheese squared, plus Juan minus t squared. Chris Eakin. Age squirt of cheese squared plus one over the squirt of t squared, plus one.

Amrita B.

Topics

Derivatives

Differentiation

Book Cover for Calculus: Early Tra…

Calculus: Early Transcendentals

Chapter 3

Differentiation Rules

Section 11

Hyperbolic Functions

Top Calculus 1 / AB Educators

Heather Z.

Oregon State University

Kayleah T.

Harvey Mudd College

Caleb E.

Baylor University

Kristen K.

University of Michigan - Ann Arbor