Find the Derivative Using Chain Rule - d/dx cube root of x

Problem

d(√(3,x))/d(x)

Solution

1. Rewrite the radical expression as a power with a fractional exponent.

√(3,x)=x(1/3)

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

d(x(1/3))/d(x)=1/3*x(1/3−1)

3. Simplify the exponent by performing the subtraction.

1/3−1=−2/3

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

1/3*x(−2/3)=1/(3*x(2/3))

Final Answer

d(√(3,x))/d(x)=1/(3√(3,x2))

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