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LET • (CX)= In [x²(x+5) ³ (x² + 4)⁰7 f'(x) = LET F(x) = \n [X²(X + 3) ³ (X² + 2)²] Cico

LET • (CX)= In [x²(x+5) ³ (x² + 4)⁰7 f'(x) = LET F(x) = \n [X²(X + 3) ³ (X² + 2)²] Cico

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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**Mathematics: Calculus and Derivation** In this exercise, you're given two functions of \( f(x) \) in logarithmic form and asked to find their derivatives, \( f'(x) \). 1. **Function 1:** \[ \text{Let } f(x) = \ln\left[x^7(x+5)^5(x^2+4)^8\right] \] Students should apply the properties of logarithms and the chain rule to differentiate this expression. The function is a composition of exponential functions within a natural logarithm, hinting at the use of the logarithmic derivative. 2. **Function 2:** \[ \text{Let } f(x) = \ln\left[x^7(x+3)^5(x^2+2)^7\right] \] Similar to the first function, the task is to differentiate using the properties of logarithms and the chain rule. These exercises emphasize the application of logarithm properties to simplify complex expressions and finding derivatives of logarithmic functions. Ensure to expand and simplify the expressions within the derivative process.
Transcribed Image Text:**Mathematics: Calculus and Derivation** In this exercise, you're given two functions of \( f(x) \) in logarithmic form and asked to find their derivatives, \( f'(x) \). 1. **Function 1:** \[ \text{Let } f(x) = \ln\left[x^7(x+5)^5(x^2+4)^8\right] \] Students should apply the properties of logarithms and the chain rule to differentiate this expression. The function is a composition of exponential functions within a natural logarithm, hinting at the use of the logarithmic derivative. 2. **Function 2:** \[ \text{Let } f(x) = \ln\left[x^7(x+3)^5(x^2+2)^7\right] \] Similar to the first function, the task is to differentiate using the properties of logarithms and the chain rule. These exercises emphasize the application of logarithm properties to simplify complex expressions and finding derivatives of logarithmic functions. Ensure to expand and simplify the expressions within the derivative process.
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