Find the derivative of the function y = 3 sec (x+7). (Use symbolic notation and fractions where needed.) 3lx+71 y = %D (x + 7)°V?. x* + 14x +48 Incorrect
Find the derivative of the function y = 3 sec (x+7). (Use symbolic notation and fractions where needed.) 3lx+71 y = %D (x + 7)°V?. x* + 14x +48 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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![**Problem:**
Find the derivative of the function \( y = 3 \sec^{-1}(x + 7) \).
(Use symbolic notation and fractions where needed.)
**Solution Attempt:**
The derivative is given by:
\[
y' = \frac{3|x + 7|}{(x + 7)^2 \sqrt{x^2 + 14x + 48}}
\]
**Feedback:**
The solution is marked as "Incorrect."
---
### Explanation:
The task is to find the derivative of the function \( y = 3 \sec^{-1}(x + 7) \). The expression for the derivative involves several components, including:
- **Numerator:** \( 3|x + 7| \)
- **Denominator:** \( (x + 7)^2 \sqrt{x^2 + 14x + 48} \)
The function inside the inverse secant, \( (x + 7) \), influences both the absolute value and the squared term in the denominator, and the quadratic expression under the square root might come from using chain or product rules incorrectly.
Consider reviewing differentiation rules for inverse trigonometric functions and reevaluating your steps.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9ff172f4-e364-41be-8a7d-a0be09aa7529%2F2554b0fb-e9f7-4535-9098-db8effbf7558%2F8wsq1rb_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem:**
Find the derivative of the function \( y = 3 \sec^{-1}(x + 7) \).
(Use symbolic notation and fractions where needed.)
**Solution Attempt:**
The derivative is given by:
\[
y' = \frac{3|x + 7|}{(x + 7)^2 \sqrt{x^2 + 14x + 48}}
\]
**Feedback:**
The solution is marked as "Incorrect."
---
### Explanation:
The task is to find the derivative of the function \( y = 3 \sec^{-1}(x + 7) \). The expression for the derivative involves several components, including:
- **Numerator:** \( 3|x + 7| \)
- **Denominator:** \( (x + 7)^2 \sqrt{x^2 + 14x + 48} \)
The function inside the inverse secant, \( (x + 7) \), influences both the absolute value and the squared term in the denominator, and the quadratic expression under the square root might come from using chain or product rules incorrectly.
Consider reviewing differentiation rules for inverse trigonometric functions and reevaluating your steps.
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