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

Problem

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

Solution

1. Identify the constant and the power of the variable in the expression 3*x(1/3)

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

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

4. Substitute n=1/3 into the power rule formula.

(d(3)*x(1/3))/d(x)=3⋅1/3*x(1/3−1)

5. Simplify the coefficient and the exponent.

3⋅1/3=1

1/3−1=−2/3

6. Rewrite the expression using the simplified values.

1*x(−2/3)=x(−2/3)

Final Answer

(d(3)*x(1/3))/d(x)=x(−2/3)

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