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If y=sec^-1{(√x 1)/√(x-1)} sin^-1{(√x-1)/(√x 1)}, then the value of dy/dx will be?
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If y=sec^-1{(√x 1)/√(x-1)} sin^-1{(√x-1)/(√x 1)}, then the value of ...
Derivation of dy/dx:
- First, let's rewrite the given functions in a more manageable form:
- Let y = sec^(-1)(√x + 1)/√(x - 1)
- And let z = sin^(-1)(√x - 1)/(√x + 1)
Finding dy/dx:
- To find dy/dx, we use the chain rule:
- dy/dx = dy/du * du/dx
- Where u = (√x + 1)/√(x - 1)
Finding dy/du:
- Differentiate y with respect to u:
- dy/du = d/dx(sec^(-1)u)
- Using the chain rule and derivative of sec^(-1)u, we get:
- dy/du = 1/(|u| * √(u^2 - 1))
Finding du/dx:
- Differentiate u with respect to x:
- du/dx = d/dx((√x + 1)/√(x - 1))
- Using the quotient rule, we get:
- du/dx = ((√(x - 1) - (√x + 1)/(2√(x - 1))) / (x - 1)
Final calculation for dy/dx:
- Now, we substitute dy/du and du/dx back into the chain rule formula:
- dy/dx = (1/(|u| * √(u^2 - 1))) * ((√(x - 1) - (√x + 1)/(2√(x - 1))) / (x - 1))
- Simplify further if needed to get the final expression for dy/dx.
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If y=sec^-1{(√x 1)/√(x-1)} sin^-1{(√x-1)/(√x 1)}, then the value of dy/dx will be?
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If y=sec^-1{(√x 1)/√(x-1)} sin^-1{(√x-1)/(√x 1)}, then the value of dy/dx will be? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about If y=sec^-1{(√x 1)/√(x-1)} sin^-1{(√x-1)/(√x 1)}, then the value of dy/dx will be? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If y=sec^-1{(√x 1)/√(x-1)} sin^-1{(√x-1)/(√x 1)}, then the value of dy/dx will be?.
If y=sec^-1{(√x 1)/√(x-1)} sin^-1{(√x-1)/(√x 1)}, then the value of dy/dx will be? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about If y=sec^-1{(√x 1)/√(x-1)} sin^-1{(√x-1)/(√x 1)}, then the value of dy/dx will be? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If y=sec^-1{(√x 1)/√(x-1)} sin^-1{(√x-1)/(√x 1)}, then the value of dy/dx will be?.
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