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

Problem

d()/d(x)√(3,x2)

Solution

1. Rewrite the radical expression using a rational exponent. The cube root of x2 is equivalent to x raised to the power of two-thirds.

√(3,x2)=x(2/3)

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

d(x(2/3))/d(x)=2/3*x(2/3−1)

3. Simplify the exponent by subtracting the values.

2/3−1=−1/3

4. Rewrite the expression using positive exponents and radical notation if desired. A negative exponent indicates a reciprocal.

2/3*x(−1/3)=2/(3*x(1/3))

2/(3*x(1/3))=2/(3√(3,x))

Final Answer

d(√(3,x2))/d(x)=2/(3√(3,x))

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