CA Foundation Exam > CA Foundation Questions > If y=(x √x^2 m^2)^n then dy/dx is equal to?
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If y=(x √x^2 m^2)^n then dy/dx is equal to?
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If y=(x √x^2 m^2)^n then dy/dx is equal to?
Derivative of y=(x √x^2 m^2)^n
- First, rewrite the given function in a more manageable form: y = x^(3/2) * m * n.
- To find the derivative, we will use the power rule and chain rule.
- Let's differentiate y with respect to x.
Applying the Power Rule
- dy/dx = d/dx (x^(3/2) * m * n)
- dy/dx = (3/2)x^(1/2) * m * n
Applying the Chain Rule
- Now, we need to apply the chain rule for the term x^(3/2):
- Let u = x^(3/2), then dy/dx = du/dx * dy/du
- du/dx = (3/2)x^(1/2)
- dy/du = m * n
Combining the Results
- Finally, we combine the results from applying the chain rule and power rule:
- dy/dx = du/dx * dy/du
- dy/dx = (3/2)x^(1/2) * m * n
Conclusion
- The derivative of y=(x √x^2 m^2)^n with respect to x is (3/2)x^(1/2) * m * n.
- First, rewrite the given function in a more manageable form: y = x^(3/2) * m * n.
- To find the derivative, we will use the power rule and chain rule.
- Let's differentiate y with respect to x.
Applying the Power Rule
- dy/dx = d/dx (x^(3/2) * m * n)
- dy/dx = (3/2)x^(1/2) * m * n
Applying the Chain Rule
- Now, we need to apply the chain rule for the term x^(3/2):
- Let u = x^(3/2), then dy/dx = du/dx * dy/du
- du/dx = (3/2)x^(1/2)
- dy/du = m * n
Combining the Results
- Finally, we combine the results from applying the chain rule and power rule:
- dy/dx = du/dx * dy/du
- dy/dx = (3/2)x^(1/2) * m * n
Conclusion
- The derivative of y=(x √x^2 m^2)^n with respect to x is (3/2)x^(1/2) * m * n.
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If y=(x √x^2 m^2)^n then dy/dx is equal to?
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If y=(x √x^2 m^2)^n then 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 y=(x √x^2 m^2)^n then 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 y=(x √x^2 m^2)^n then dy/dx is equal to?.
If y=(x √x^2 m^2)^n then 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 y=(x √x^2 m^2)^n then 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 y=(x √x^2 m^2)^n then dy/dx is equal to?.
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