SOLVED:Find The Derivative. Simplify Where Possible. G(t) = \sinh (\ln T)

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Find the derivative. Simplify where possible. $ G(t) = \sinh (\ln t) $ Find the derivative. Simplify where possible.$ G(t) = \sinh (\ln t) $ Calculus: Early Transcendentals Calculus: Early Transcendentals James Stewart 8th Edition Chapter 3, Problem 35 ↓ View All Chapters

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Thumb up icon Thumb down icon Submit Thanks for your feedback! Profile picture Find the derivative. Simplify where possible. $ G(t) = \sinh (\ln t) $ Close icon Play audio Feedback Upload button Send button Powered by NumerAI David Collins Danielle Fairburn Ivan Kochetkov verified

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Key Concepts

- Chain Rule The chain rule is a fundamental differentiation technique used to compute the derivative of a composite function. It states that if one function is applied to the result of another function, the derivative of the overall function is the derivative of the outer function evaluated at the inner function, multiplied by the derivative of the inner function. Derivative of Hyperbolic Functions Hyperbolic functions, such as the hyperbolic sine function (sinh), have their own differentiation rules. The derivative of sinh(x) is cosh(x), which is analogous to the differentiation rule for trigonometric sine functions but pertains to their hyperbolic counterparts. Derivative of the Natural Logarithm Function The natural logarithm function (ln) is a common function in calculus with the derivative 1/t when expressed in terms of t. This derivative plays a crucial role when differentiating functions where ln appears as an inner function in a composite setting. Simplification of Composed Functions Simplification in the context of composed functions involves applying differentiation rules, such as the chain rule, and then rewriting the result in the simplest form possible. This often means cancelling common factors or rewriting expressions compactly to communicate the derivative in a clear and concise way. Key Concept Premium Feature Explore the core concept behind this problem. View Video Play button 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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- 00:01 Given the chain rule and the fact that u is the natural log of t, therefore g of u is sign h of u... 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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