Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN: 9781285741550
Author: James Stewart
Publisher: Cengage Learning
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## Calculating Higher Derivatives Consider the function: \[ y = 7e^t \sin(t) \] We are required to calculate the higher derivatives of this function. Use symbolic notation and fractions where needed. ### First Derivative \[ y' = \frac{d}{dt}(7e^t \sin(t)) \] (Note that the product rule must be applied here because the function is a product of \( 7e^t \) and \( \sin(t) \).) ### Second Derivative Your calculated derivative is: \[ y'' = \frac{d}{dt}(7e^t \sin(t)) \] However, the solution provided: \[ y'' = \frac{e^t(-\cos(t)) - e^t \sin(x)} \] is marked as incorrect. ### Third Derivative There is an input field for the third derivative, \( y''' = \), which remains unfilled. Any incorrect input here would also receive the Incorrect mark. Please ensure that while calculating the derivatives, the product rule and chain rule are correctly applied.
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Transcribed Image Text:## Calculating Higher Derivatives Consider the function: \[ y = 7e^t \sin(t) \] We are required to calculate the higher derivatives of this function. Use symbolic notation and fractions where needed. ### First Derivative \[ y' = \frac{d}{dt}(7e^t \sin(t)) \] (Note that the product rule must be applied here because the function is a product of \( 7e^t \) and \( \sin(t) \).) ### Second Derivative Your calculated derivative is: \[ y'' = \frac{d}{dt}(7e^t \sin(t)) \] However, the solution provided: \[ y'' = \frac{e^t(-\cos(t)) - e^t \sin(x)} \] is marked as incorrect. ### Third Derivative There is an input field for the third derivative, \( y''' = \), which remains unfilled. Any incorrect input here would also receive the Incorrect mark. Please ensure that while calculating the derivatives, the product rule and chain rule are correctly applied.
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