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

Problem

d()/d(x)*(x(1/3)+1)

Solution

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

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

2. Apply the power rule to the first term, where d(xn)/d(x)=n*x(n−1) with n=1/3

d(x(1/3))/d(x)=1/3*x(1/3−1)

3. Simplify the exponent by performing the subtraction.

1/3*x(1/3−3/3)=1/3*x(−2/3)

4. Apply the constant rule to the second term, noting that the derivative of any constant is zero.

d(1)/d(x)=0

5. Combine the results to find the final derivative.

1/3*x(−2/3)+0=1/(3*x(2/3))

Final Answer

d()/d(x)*(x(1/3)+1)=1/(3*x(2/3))

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