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If y=x2/3 then dy/dx?
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If y=x2/3 then dy/dx?
Calculation of dy/dx for y=x2/3
To calculate the derivative of y with respect to x, we need to use the power rule of differentiation. The power rule states that for any function of the form x^n, the derivative with respect to x is n*x^(n-1). Using this rule, we can find the derivative of y with respect to x as follows:
Explanation of the Solution
The given function y=x2/3 can be rewritten as y=x^(2/3) using exponentiation. To find the derivative of y with respect to x, we use the power rule of differentiation. This rule states that if we have a function of the form x^n, the derivative with respect to x is n*x^(n-1).
Applying the power rule to our function, we get dy/dx = (2/3)*x^(-1/3). We can simplify this expression by combining the exponent terms as follows: dy/dx = 2/(3*x^(1/3)).
Therefore, the derivative of y=x2/3 with respect to x is dy/dx = 2/(3*x^(1/3)).
To calculate the derivative of y with respect to x, we need to use the power rule of differentiation. The power rule states that for any function of the form x^n, the derivative with respect to x is n*x^(n-1). Using this rule, we can find the derivative of y with respect to x as follows:
- First, rewrite y=x2/3 as y=x^(2/3).
- Next, apply the power rule to find the derivative: dy/dx = (2/3)*x^(-1/3).
- Finally, simplify the expression by combining the exponent terms: dy/dx = 2/(3*x^(1/3)).
Explanation of the Solution
The given function y=x2/3 can be rewritten as y=x^(2/3) using exponentiation. To find the derivative of y with respect to x, we use the power rule of differentiation. This rule states that if we have a function of the form x^n, the derivative with respect to x is n*x^(n-1).
Applying the power rule to our function, we get dy/dx = (2/3)*x^(-1/3). We can simplify this expression by combining the exponent terms as follows: dy/dx = 2/(3*x^(1/3)).
Therefore, the derivative of y=x2/3 with respect to x is dy/dx = 2/(3*x^(1/3)).
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If y=x2/3 then dy/dx?
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If y=x2/3 then dy/dx? for CA Foundation 2025 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about If y=x2/3 then dy/dx? covers all topics & solutions for CA Foundation 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If y=x2/3 then dy/dx?.
If y=x2/3 then dy/dx? for CA Foundation 2025 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about If y=x2/3 then dy/dx? covers all topics & solutions for CA Foundation 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If y=x2/3 then dy/dx?.
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