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

Problem

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

Solution

1. Identify the form of the function, which is a power function xn where n=3/2

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

3. Substitute the value of n into the formula to get 3/2*x(3/2−1)

4. Simplify the exponent by calculating 3/2−1=1/2

Final Answer

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

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