Find the Derivative - d/d@VAR f(x)=3/( cube root of x)

Problem

d()/d(x)3/√(3,x)

Solution

1. Rewrite the expression using exponents to prepare for differentiation.

ƒ(x)=3*x(−1/3)

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

d(ƒ(x))/d(x)=3⋅(−1/3)*x(−1/3−1)

3. Simplify the coefficient and the exponent.

d(ƒ(x))/d(x)=−1*x(−4/3)

4. Convert the expression back into radical form with a positive exponent.

d(ƒ(x))/d(x)=−1/(x(4/3))

d(ƒ(x))/d(x)=−1/√(3,x4)

Final Answer

d()/d(x)3/√(3,x)=−1/√(3,x4)

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