Find 이승 dy dx y=3(secx + tan x)(secx- tan x) 11 ***

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...
icon
Related questions
Question
**Problem Statement:**

Find \(\frac{dy}{dx}\), where:

\[ y = 3(\sec x + \tan x)(\sec x - \tan x) \]

---

**Solution:**

To find \(\frac{dy}{dx}\), we will need to first expand the expression for \(y\):

\[ y = 3[(\sec x + \tan x)(\sec x - \tan x)] \]

Using the identity \((a+b)(a-b) = a^2 - b^2\), we have:

\[ y = 3(\sec^2 x - \tan^2 x) \]

Next, we'll use the identity \(\sec^2 x - \tan^2 x = 1\):

\[ y = 3 \times 1 = 3 \]

Now, since \(y\) is a constant, the derivative \(\frac{dy}{dx} = 0\).

Therefore, \(\frac{dy}{dx} = \boxed{0}\).
Transcribed Image Text:**Problem Statement:** Find \(\frac{dy}{dx}\), where: \[ y = 3(\sec x + \tan x)(\sec x - \tan x) \] --- **Solution:** To find \(\frac{dy}{dx}\), we will need to first expand the expression for \(y\): \[ y = 3[(\sec x + \tan x)(\sec x - \tan x)] \] Using the identity \((a+b)(a-b) = a^2 - b^2\), we have: \[ y = 3(\sec^2 x - \tan^2 x) \] Next, we'll use the identity \(\sec^2 x - \tan^2 x = 1\): \[ y = 3 \times 1 = 3 \] Now, since \(y\) is a constant, the derivative \(\frac{dy}{dx} = 0\). Therefore, \(\frac{dy}{dx} = \boxed{0}\).
Expert Solution
Step 1

Calculus homework question answer, step 1, image 1

steps

Step by step

Solved in 2 steps with 2 images

Blurred answer
Recommended textbooks for you
Calculus: Early Transcendentals
Calculus: Early Transcendentals
Calculus
ISBN:
9781285741550
Author:
James Stewart
Publisher:
Cengage Learning
Thomas' Calculus (14th Edition)
Thomas' Calculus (14th Edition)
Calculus
ISBN:
9780134438986
Author:
Joel R. Hass, Christopher E. Heil, Maurice D. Weir
Publisher:
PEARSON
Calculus: Early Transcendentals (3rd Edition)
Calculus: Early Transcendentals (3rd Edition)
Calculus
ISBN:
9780134763644
Author:
William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz
Publisher:
PEARSON
Calculus: Early Transcendentals
Calculus: Early Transcendentals
Calculus
ISBN:
9781319050740
Author:
Jon Rogawski, Colin Adams, Robert Franzosa
Publisher:
W. H. Freeman
Precalculus
Precalculus
Calculus
ISBN:
9780135189405
Author:
Michael Sullivan
Publisher:
PEARSON
Calculus: Early Transcendental Functions
Calculus: Early Transcendental Functions
Calculus
ISBN:
9781337552516
Author:
Ron Larson, Bruce H. Edwards
Publisher:
Cengage Learning