Find the Derivative - d/dx 3/2x^(2/3)

Problem

d()/d(x)3/2*x(2/3)

Solution

1. Identify the constant and the power of x in the expression. The expression is in the form c⋅xn where c=3/2 and n=2/3

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

3. Multiply the constant 3/2 by the exponent 2/3

3/2⋅2/3=1

4. Subtract 1 from the exponent to find the new power.

2/3−1=−1/3

5. Combine the results to write the final derivative.

d()/d(x)3/2*x(2/3)=1⋅x(−1/3)

Final Answer

d()/d(x)3/2*x(2/3)=x(−1/3)

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