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

Problem

d()/d(x)(x2)/3

Solution

1. Identify the constant factor in the expression. The expression (x2)/3 can be rewritten as 1/3⋅x2

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

3. Differentiate the term x2 using the power rule, d(xn)/d(x)=n*x(n−1)

4. Multiply the constant 1/3 by the result of the derivative, 2*x

5. Simplify the resulting expression into a single fraction.

Final Answer

d()/d(x)(x2)/3=(2*x)/3

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