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

Problem

d()/d(x)*(x−3*x(1/3))

Solution

1. Apply the sum rule for differentiation, which states that the derivative of a sum or difference is the sum or difference of the derivatives.

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

2. Apply the power rule to the first term, where the derivative of xn is n*x(n−1)

d(x)/d(x)=1

3. Apply the constant multiple rule and the power rule to the second term.

(d(3)*x(1/3))/d(x)=3⋅1/3*x(1/3−1)

4. Simplify the coefficients and the exponent in the second term.

3⋅1/3*x(−2/3)=x(−2/3)

5. Combine the results of the differentiated terms.

1−x(−2/3)

Final Answer

d()/d(x)*(x−3*x(1/3))=1−x(−2/3)

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