Find the Derivative - d/dx cube root of x^2

Problem

d(√(3,x^2))/d(x)

Solution

1. Rewrite the radical expression using a rational exponent by applying the rule √(n,x^m)=x^m/n

√(3,x^2)=x^2/3

2. Apply the power rule for differentiation, which states d(x^n)/d(x)=n*x^(n−1)

d(x^2/3)/d(x)=2/3*x^(2/3−1)

3. Simplify the exponent by performing the subtraction.

2/3−1=−1/3

4. Rewrite the expression using positive exponents and radical notation if desired.

2/3*x^(−1/3)=2/(3*x^1/3)

2/(3*x^1/3)=2/(3√(3,x))

Final Answer

d(√(3,x^2))/d(x)=2/(3√(3,x))

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