Computer Science Engineering (CSE) Exam > Computer Science Engineering (CSE) Questions > If u=log (x^2 y^2) then x du/dx y du/dy=.?
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If u=log (x^2 y^2) then x du/dx y du/dy=.?
Most Upvoted Answer
If u=log (x^2 y^2) then x du/dx y du/dy=.?
Explanation:
Given: u = log(x^2 y^2)
- We need to find x * du/dx + y * du/dy
Chain Rule:
- The chain rule states that if u = f(g(x)), then du/dx = f'(g(x)) * g'(x)
Applying Chain Rule:
- Here, u = log(x^2 y^2)
- Let's consider f(z) = log(z) where z = x^2 y^2
- f'(z) = 1/z
Partial Derivatives:
- To find du/dx and du/dy, we need to take partial derivatives
- du/dx = f'(z) * d/dx (x^2 y^2)
= 1/(x^2 y^2) * 2x * y^2
= 2y/x
- du/dy = f'(z) * d/dy (x^2 y^2)
= 1/(x^2 y^2) * 2y * x^2
= 2x/y
Final Calculation:
- x * du/dx + y * du/dy
= x * (2y/x) + y * (2x/y)
= 2y + 2x
= 2(x + y)
Conclusion:
- Therefore, x * du/dx + y * du/dy = 2(x + y)
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If u=log (x^2 y^2) then x du/dx y du/dy=.? for Computer Science Engineering (CSE) 2024 is part of Computer Science Engineering (CSE) preparation. The Question and answers have been prepared according to the Computer Science Engineering (CSE) exam syllabus. Information about If u=log (x^2 y^2) then x du/dx y du/dy=.? covers all topics & solutions for Computer Science Engineering (CSE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If u=log (x^2 y^2) then x du/dx y du/dy=.?.
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