CA Foundation Exam > CA Foundation Questions > If y=e^x e^-x then dy/dx-√y^2-4 is equal to?
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If y=e^x e^-x then dy/dx-√y^2-4 is equal to?
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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.
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If y=e^x e^-x then dy/dx-√y^2-4 is equal to?
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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?.
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