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Determine t'(x) if t(x) = 7(3*). Select the correct answer below: O t'(x) = 7(3³) O t'(x) = 3' ln x O t'(x) = 3 (3ln 7) O t'(x) = 3 (7ln 3) O t'(x) = (7x)3x-1

Determine t'(x) if t(x) = 7(3*). Select the correct answer below: O t'(x) = 7(3³) O t'(x) = 3' ln x O t'(x) = 3 (3ln 7) O t'(x) = 3 (7ln 3) O t'(x) = (7x)3x-1

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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**Differentiation Problem: Finding the Derivative** **Question:** Determine \( t'(x) \) if \( t(x) = 7(3^x) \). **Answer Choices:** Select the correct answer below: - \( \circ \quad t'(x) = 7(3^x) \) - \( \circ \quad t'(x) = 3^x \ln x \) - \( \circ \quad t'(x) = 3^x (3 \ln 7) \) - \( \circ \quad t'(x) = 3^x (7 \ln 3) \) - \( \circ \quad t'(x) = (7x)3^{x-1} \) **Answer Explanation:** To find the correct derivative \( t'(x) \), apply the chain rule and the formula for the derivative of the exponential function \( a^{x} \). The differentiation of \( t(x) = 7(3^x) \) results in: \[ t'(x) = 7 \cdot \frac{d}{dx}(3^x) \] Using the exponential differentiation rule \( \frac{d}{dx}(a^x) = a^x \ln a \), we get: \[ t'(x) = 7 \cdot 3^x \ln 3 \] Therefore, the correct answer is: \[ \boxed{t'(x) = 7 \cdot 3^x \ln 3} \] So, select the answer choice with the same expression as derived above. The selection above suggests that the correct answer is: \[ t'(x) = 3^x (7 \ln 3) \]
Transcribed Image Text:**Differentiation Problem: Finding the Derivative** **Question:** Determine \( t'(x) \) if \( t(x) = 7(3^x) \). **Answer Choices:** Select the correct answer below: - \( \circ \quad t'(x) = 7(3^x) \) - \( \circ \quad t'(x) = 3^x \ln x \) - \( \circ \quad t'(x) = 3^x (3 \ln 7) \) - \( \circ \quad t'(x) = 3^x (7 \ln 3) \) - \( \circ \quad t'(x) = (7x)3^{x-1} \) **Answer Explanation:** To find the correct derivative \( t'(x) \), apply the chain rule and the formula for the derivative of the exponential function \( a^{x} \). The differentiation of \( t(x) = 7(3^x) \) results in: \[ t'(x) = 7 \cdot \frac{d}{dx}(3^x) \] Using the exponential differentiation rule \( \frac{d}{dx}(a^x) = a^x \ln a \), we get: \[ t'(x) = 7 \cdot 3^x \ln 3 \] Therefore, the correct answer is: \[ \boxed{t'(x) = 7 \cdot 3^x \ln 3} \] So, select the answer choice with the same expression as derived above. The selection above suggests that the correct answer is: \[ t'(x) = 3^x (7 \ln 3) \]
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