SOLVED:Find The Derivative. Simplify Where Possible. F(x) = \tanh ...

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Find the derivative. Simplify where possible. $ f(x) = \tanh \sqrt x $ Find the derivative. Simplify where possible.$ f(x) = \tanh \sqrt x $ Calculus: Early Transcendentals James Stewart 8th Edition Chapter 3, Problem 31 View All Chapters

Step 1

The chain rule states that the derivative of a composite function is the derivative of the outer function times the derivative of the inner function. Show more…

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Key Concepts

Chain Rule The chain rule is used when differentiating composite functions. It states that the derivative of a composition of functions is the derivative of the outer function evaluated at the inner function times the derivative of the inner function. Derivative of Hyperbolic Tangent In differentiation, the hyperbolic tangent function, tanh(x), has the derivative sech²(x). Recognizing this derivative is essential when working with functions involving hyperbolic trigonometric functions. Differentiating Radical Functions The square root function can be expressed as x^(1/2), and its derivative is found using the power rule, resulting in 1/(2?x). This technique is fundamental for differentiating any function involving radicals. Key Concept Premium Feature Explore the core concept behind this problem. View Video View Video Key Concept Premium Feature Explore the core concept behind this problem. Your browser does not support the video tag. Close Try it Now

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Transcript

00:01 We have a question in which we need to find the derivative of f x equal to 10 and root x we know that derivative of 10x d by d x 10 x 10 x equal to sq square x x okay this is the hyperbolic function so if we do like this, so f -dash -x will be sig square x into differentiation of this under root x with respect to x 1 by 2 x raised to the power 1 by 2 minus 1. 00:56 So this will become 1 by 2 under root x into 6 square under root x... Need help? Use Ace Ace is your personal tutor. It breaks down any question with clear steps so you can learn. Start Using Ace Ace is your personal tutor for learning Step-by-step explanations Instant summaries Summarize YouTube videos Understand textbook images or PDFs Study tools like quizzes and flashcards Listen to your notes as a podcast

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