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
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:
\[ t'(x) = 3^x (7 \ln 3) \]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb0e32857-51d2-44a4-8f71-ebf2e20ef78a%2F8919b216-e6a1-4bb0-a023-7bee9122784b%2Ffn0egnq_processed.jpeg&w=3840&q=75)
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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