Calculate the higher derivatives. y = 7e¹ sin(t) (Use symbolic notation and fractions where needed.) y" =_e¹ (−cos (t)) – e¹ sin(x) Incorrect y"" = Incorrect
Calculate the higher derivatives. y = 7e¹ sin(t) (Use symbolic notation and fractions where needed.) y" =_e¹ (−cos (t)) – e¹ sin(x) Incorrect y"" = Incorrect
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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![## 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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F575d721b-26eb-4db6-af93-50c207cd3fab%2Ffc5a6e2e-df74-4797-9129-9542a1f41425%2F0lny6h_processed.jpeg&w=3840&q=75)
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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