Find the Derivative - d/dx x^(1/3)

Problem

d(x(1/3))/d(x)

Solution

1. Identify the rule needed for differentiation, which is the Power Rule.

2. Apply the formula for the Power Rule, which states that d(xn)/d(x)=n*x(n−1)

3. Substitute n=1/3 into the formula.

4. Subtract 1 from the exponent: 1/3 - 1 = -2/3$.

5. Simplify the expression by writing the result with the new coefficient and exponent.

Final Answer

d(x(1/3))/d(x)=1/3*x(−2/3)

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