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dy Find when dx x(t) = 3te, y(t) = 4tet. 1. 2. 3. 4. dy dx dy dx dy dx dy dx 3e¹(1+t) 4 + et 3e (1 t) 4 + et 4- et 3et (1+t) 4- et 3et (1 t)

dy Find when dx x(t) = 3te, y(t) = 4tet. 1. 2. 3. 4. dy dx dy dx dy dx dy dx 3e¹(1+t) 4 + et 3e (1 t) 4 + et 4- et 3et (1+t) 4- et 3et (1 t)

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Certainly! Below is the transcription suitable for an educational website. --- ### Derivatives of Functions Involving Exponential Terms 5. \(\frac{dy}{dx} = \frac{4 + e^t}{3e^t(1 - t)}\) 6. \(\frac{dy}{dx} = \frac{3e^t(1 + t)}{4 - e^t}\) In these examples, we are dealing with derivatives of functions that include exponential terms. The notation \(\frac{dy}{dx}\) represents the derivative of \(y\) with respect to \(x\). For equation 5, the derivative \(\frac{dy}{dx}\) is expressed as a fraction, where the numerator is \(4 + e^t\) and the denominator is \(3e^t(1 - t)\). For equation 6, the derivative \(\frac{dy}{dx}\) also takes the form of a fraction with the numerator \(3e^t(1 + t)\), and the denominator \(4 - e^t\). Understanding these expressions helps in the study of how functions change and is a fundamental aspect of calculus.
Transcribed Image Text:Certainly! Below is the transcription suitable for an educational website. --- ### Derivatives of Functions Involving Exponential Terms 5. \(\frac{dy}{dx} = \frac{4 + e^t}{3e^t(1 - t)}\) 6. \(\frac{dy}{dx} = \frac{3e^t(1 + t)}{4 - e^t}\) In these examples, we are dealing with derivatives of functions that include exponential terms. The notation \(\frac{dy}{dx}\) represents the derivative of \(y\) with respect to \(x\). For equation 5, the derivative \(\frac{dy}{dx}\) is expressed as a fraction, where the numerator is \(4 + e^t\) and the denominator is \(3e^t(1 - t)\). For equation 6, the derivative \(\frac{dy}{dx}\) also takes the form of a fraction with the numerator \(3e^t(1 + t)\), and the denominator \(4 - e^t\). Understanding these expressions helps in the study of how functions change and is a fundamental aspect of calculus.
**Problem: Find \(\frac{dy}{dx}\) when** \(x(t) = 3te^t, \quad y(t) = 4t - e^t.\) **Options:** 1. \(\frac{dy}{dx} = \frac{3e^t(1 + t)}{4 + e^t}\) 2. \(\frac{dy}{dx} = \frac{3e^t(1 - t)}{4 + e^t}\) 3. \(\frac{dy}{dx} = \frac{4 - e^t}{3e^t(1 + t)}\) 4. \(\frac{dy}{dx} = \frac{4 - e^t}{3e^t(1 - t)}\)
Transcribed Image Text:**Problem: Find \(\frac{dy}{dx}\) when** \(x(t) = 3te^t, \quad y(t) = 4t - e^t.\) **Options:** 1. \(\frac{dy}{dx} = \frac{3e^t(1 + t)}{4 + e^t}\) 2. \(\frac{dy}{dx} = \frac{3e^t(1 - t)}{4 + e^t}\) 3. \(\frac{dy}{dx} = \frac{4 - e^t}{3e^t(1 + t)}\) 4. \(\frac{dy}{dx} = \frac{4 - e^t}{3e^t(1 - t)}\)
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