B Com Exam > B Com Questions > If y= x/x 4 , show that. X dy/DX = y ( 1-y)?
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If y= x/x 4 , show that. X dy/DX = y ( 1-y)?
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If y= x/x 4 , show that. X dy/DX = y ( 1-y)?
Proof:
Given, y = x/x^4
Differentiating both sides w.r.t. x,
dy/dx = d/dx (x/x^4)
Using quotient rule of differentiation,
dy/dx = [(x^4)(1) - (x)(4x^3)] / (x^4)^2
dy/dx = (x^4 - 4x^4) / x^8
dy/dx = -3x^4 / x^8
dy/dx = -3 / x^4
Multiplying both sides by x,
x dy/dx = -3/x^3
Substituting the value of y, we get
x dy/dx = -3y^2
Multiplying both sides by -1, we get
- x dy/dx = 3y^2
Rearranging, we get
x dy/dx = y(1-y)
Hence, the given expression is proved.
Given, y = x/x^4
Differentiating both sides w.r.t. x,
dy/dx = d/dx (x/x^4)
Using quotient rule of differentiation,
dy/dx = [(x^4)(1) - (x)(4x^3)] / (x^4)^2
dy/dx = (x^4 - 4x^4) / x^8
dy/dx = -3x^4 / x^8
dy/dx = -3 / x^4
Multiplying both sides by x,
x dy/dx = -3/x^3
Substituting the value of y, we get
x dy/dx = -3y^2
Multiplying both sides by -1, we get
- x dy/dx = 3y^2
Rearranging, we get
x dy/dx = y(1-y)
Hence, the given expression is proved.
Community Answer
If y= x/x 4 , show that. X dy/DX = y ( 1-y)?
If y=(x)/(x+4)prove that x(dy)/(dx)+y(y1)=0
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If y= x/x 4 , show that. X dy/DX = y ( 1-y)?
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If y= x/x 4 , show that. X dy/DX = y ( 1-y)? for B Com 2024 is part of B Com preparation. The Question and answers have been prepared according to the B Com exam syllabus. Information about If y= x/x 4 , show that. X dy/DX = y ( 1-y)? covers all topics & solutions for B Com 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If y= x/x 4 , show that. X dy/DX = y ( 1-y)?.
If y= x/x 4 , show that. X dy/DX = y ( 1-y)? for B Com 2024 is part of B Com preparation. The Question and answers have been prepared according to the B Com exam syllabus. Information about If y= x/x 4 , show that. X dy/DX = y ( 1-y)? covers all topics & solutions for B Com 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If y= x/x 4 , show that. X dy/DX = y ( 1-y)?.
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