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

Problem

d()/d(x)(x3)/3

Solution

1. Identify the function as a power function multiplied by a constant coefficient, where y=1/3*x3

2. Apply the constant multiple rule, which states that the derivative of c⋅ƒ(x) is c⋅ƒ(x)′

3. Apply the power rule to the term x3 which states that d(xn)/d(x)=n*x(n−1)

4. Multiply the constant 1/3 by the result of the power rule, 3*x2

5. Simplify the expression by canceling the common factor of 3

Final Answer

d()/d(x)(x3)/3=x2

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