Find the derivative of y with respect to the appropriate variable. y=2 √(t) tanh√(t)

Name: Problem 15, Chapter 7: University Calculus: Early Transcendentals
Uploaded: 2020-04-15T12:40:23-08:00
Duration: 2 min 4 s
Channel: Matthew Allcock
Description: Find the derivative of y with respect to the appropriate variable. y=2 √(t) tanh√(t)

step 1 In this video, we're going to go through the answer to question number 15 from chapter 7 .3. So

Find the derivative of y with respect to the appropriate...

Key Concepts

Derivative of Hyperbolic Tangent Function

Hyperbolic functions are analogs of trigonometric functions related to the hyperbola. The derivative of the hyperbolic tangent function, tanh(u), with respect to u is sech^2(u), where sech is the hyperbolic secant function. This result is important when differentiating functions that incorporate hyperbolic trigonometry.

Derivative of Square Root Function

The square root function is an example of a power function, specifically expressed as t^(1/2). Its derivative involves applying the power rule: the derivative of t^(1/2) is (1/2)t^(-1/2). This concept is fundamental in differentiating functions where square roots are present.

Derivative

The process of finding the derivative involves determining the rate at which a function changes with respect to its independent variable. This is a fundamental concept in calculus used to understand the behavior of functions and compute slopes of tangent lines at specific points.

Product Rule

The product rule is a technique used in differentiation when dealing with the product of two functions. It states that the derivative of a product f(t)g(t) is f'(t)g(t) + f(t)g'(t), allowing for systematic computation of derivatives where the function is expressed as a product.

Chain Rule

The chain rule is employed when differentiating composite functions, where one function is nested inside another. It provides a method to differentiate by taking the derivative of the outer function and then multiplying it by the derivative of the inner function, which is essential when functions involve transformations like square roots or other non-trivial operations.

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