CA Foundation Exam > CA Foundation Questions > If y=e^x e^-x then dy/dx-√y^2-4 is equal to?
Start Learning for Free
If y=e^x e^-x then dy/dx-√y^2-4 is equal to?
Most Upvoted Answer
If y=e^x e^-x then dy/dx-√y^2-4 is equal to?
Solution:
Given, y = e^x e^-x
Taking logarithm on both sides,
ln y = ln (e^x e^-x)
ln y = x - x
ln y = 0
y = e^0
y = 1
Differentiating both sides with respect to x,
y = e^x e^-x
dy/dx = (d/dx)(e^x e^-x)
dy/dx = e^x (-e^-x) + e^-x (e^x)
dy/dx = 0
Finding the value of √y^2-4,
y^2 - 4 = (e^x e^-x)^2 - 4
y^2 - 4 = e^2x - 4
y^2 - 4 = e^2x - e^2x + 1-4
y^2 - 4 = -3
y^2 = 1
y = ±1
As y cannot be negative,
y = 1
Substituting the values of dy/dx and y in dy/dx-√y^2-4,
dy/dx - √y^2-4 = 0 - √(1^2-4)
dy/dx - √y^2-4 = -√3
Hence, dy/dx - √y^2-4 = -√3.
Given, y = e^x e^-x
Taking logarithm on both sides,
ln y = ln (e^x e^-x)
ln y = x - x
ln y = 0
y = e^0
y = 1
Differentiating both sides with respect to x,
y = e^x e^-x
dy/dx = (d/dx)(e^x e^-x)
dy/dx = e^x (-e^-x) + e^-x (e^x)
dy/dx = 0
Finding the value of √y^2-4,
y^2 - 4 = (e^x e^-x)^2 - 4
y^2 - 4 = e^2x - 4
y^2 - 4 = e^2x - e^2x + 1-4
y^2 - 4 = -3
y^2 = 1
y = ±1
As y cannot be negative,
y = 1
Substituting the values of dy/dx and y in dy/dx-√y^2-4,
dy/dx - √y^2-4 = 0 - √(1^2-4)
dy/dx - √y^2-4 = -√3
Hence, dy/dx - √y^2-4 = -√3.
Attention CA Foundation Students!
To make sure you are not studying endlessly, EduRev has designed CA Foundation study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in CA Foundation.
|
Explore Courses for CA Foundation exam
|
|
Top Courses for CA FoundationView all
If y=e^x e^-x then dy/dx-√y^2-4 is equal to?
Question Description
If y=e^x e^-x then dy/dx-√y^2-4 is equal to? for CA Foundation 2024 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about If y=e^x e^-x then dy/dx-√y^2-4 is equal to? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If y=e^x e^-x then dy/dx-√y^2-4 is equal to?.
If y=e^x e^-x then dy/dx-√y^2-4 is equal to? for CA Foundation 2024 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about If y=e^x e^-x then dy/dx-√y^2-4 is equal to? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If y=e^x e^-x then dy/dx-√y^2-4 is equal to?.
Solutions for If y=e^x e^-x then dy/dx-√y^2-4 is equal to? in English & in Hindi are available as part of our courses for CA Foundation.
Download more important topics, notes, lectures and mock test series for CA Foundation Exam by signing up for free.
Here you can find the meaning of If y=e^x e^-x then dy/dx-√y^2-4 is equal to? defined & explained in the simplest way possible. Besides giving the explanation of
If y=e^x e^-x then dy/dx-√y^2-4 is equal to?, a detailed solution for If y=e^x e^-x then dy/dx-√y^2-4 is equal to? has been provided alongside types of If y=e^x e^-x then dy/dx-√y^2-4 is equal to? theory, EduRev gives you an
ample number of questions to practice If y=e^x e^-x then dy/dx-√y^2-4 is equal to? tests, examples and also practice CA Foundation tests.
|
|
Explore Courses for CA Foundation exam
|
|
Suggested Free Tests
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup