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

Problem

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

Solution

1. Identify the constant factor in the expression. The expression (x3)/3 can be rewritten as 1/3⋅x3

2. Apply the constant multiple rule for derivatives, which states that d()/d(x)*[c⋅ƒ(x)]=c⋅d(ƒ(x))/d(x)

d()/d(x)(x3)/3=1/3⋅d(x3)/d(x)

3. Apply the power rule, d(xn)/d(x)=n*x(n−1) where n=3

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

4. Multiply the constant factor by the result of the power rule.

1/3⋅3*x2=x2

Final Answer

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

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