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9. Find f(35) (x) for f(x) = cos (2x)T = COS

9. Find f(35) (x) for f(x) = cos (2x)T = COS

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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### Problem Statement #### Given Functions: (a) \( f(x) = x \cdot 3^{2x} \) (b) \( g(t) = \log_2 \sqrt{x^2 - 1} \) #### Task: 9. Find \( f^{(35)}(x) \) for \( f(x) = \cos(2x) \). --- ### Description In this exercise, you are given two initial functions and a task. The first function, \( f(x) \), is a product of a linear term and an exponential term with base 3 raised to the power of \( 2x \). The second function, \( g(t) \), involves a logarithm base 2 applied to the square root of the expression \( x^2 - 1 \). The task requires you to determine the 35th derivative of the trigonometric function \( \cos(2x) \). This requires understanding patterns in the derivatives of trigonometric functions. This problem is ideal for practicing differentiation, specifically working with higher order derivatives and trigonometric identities.
Transcribed Image Text:### Problem Statement #### Given Functions: (a) \( f(x) = x \cdot 3^{2x} \) (b) \( g(t) = \log_2 \sqrt{x^2 - 1} \) #### Task: 9. Find \( f^{(35)}(x) \) for \( f(x) = \cos(2x) \). --- ### Description In this exercise, you are given two initial functions and a task. The first function, \( f(x) \), is a product of a linear term and an exponential term with base 3 raised to the power of \( 2x \). The second function, \( g(t) \), involves a logarithm base 2 applied to the square root of the expression \( x^2 - 1 \). The task requires you to determine the 35th derivative of the trigonometric function \( \cos(2x) \). This requires understanding patterns in the derivatives of trigonometric functions. This problem is ideal for practicing differentiation, specifically working with higher order derivatives and trigonometric identities.
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