Find the Derivative - d/dx y=x^(5/3)-x^(2/3)

Problem

d()/d(x)*(x^(5/3)−x^(2/3))

Solution

1. Identify the rule needed for differentiation, which is the Power Rule: d(x^n)/d(x)=n*x^(n−1)

2. Apply the Sum/Difference Rule to differentiate each term of the expression individually.

3. Differentiate the first term x^(5/3) by multiplying by the exponent and subtracting 1 from the exponent: 5/3*x^(5/3−1)=5/3*x^(2/3)

4. Differentiate the second term x^(2/3) by multiplying by the exponent and subtracting 1 from the exponent: 2/3*x^(2/3−1)=2/3*x^(−1/3)

5. Combine the results to find the final derivative.

Final Answer

d()/d(x)*(x^(5/3)−x^(2/3))=5/3*x^(2/3)−2/3*x^(−1/3)

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