CA Foundation Exam > CA Foundation Questions > If xy=1 then y^2 dy÷dx is equal to ?
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If xy=1 then y^2 dy÷dx is equal to ?
Most Upvoted Answer
If xy=1 then y^2 dy÷dx is equal to ?
Explanation:
Given, xy = 1
To find, y^2 dy/dx
Step 1: Differentiate both sides with respect to x
Using the product rule of differentiation, we get:
(d/dx)xy = (d/dx)1
On simplification, we get:
y(dx/dx) + x(dy/dx) = 0
dy/dx = -y/x
Step 2: Substitute the value of y in terms of x
From the given equation, xy = 1, we get:
y = 1/x
Substituting this value in dy/dx, we get:
dy/dx = -1/x^2
Step 3: Find y^2 dy/dx
Substituting the value of y in terms of x in y^2 dy/dx, we get:
y^2 dy/dx = (1/x^2)(1/x^2)
y^2 dy/dx = 1/x^4
Final Answer:
Therefore, y^2 dy/dx = 1/x^4 when xy = 1.
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If xy=1 then y^2 dy÷dx is equal to ?
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If xy=1 then y^2 dy÷dx 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 xy=1 then y^2 dy÷dx is equal to ? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If xy=1 then y^2 dy÷dx is equal to ?.
If xy=1 then y^2 dy÷dx 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 xy=1 then y^2 dy÷dx is equal to ? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If xy=1 then y^2 dy÷dx is equal to ?.
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