Find the Derivative - d/d@VAR f(x)=x^(3/2)

Problem

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

Solution

1. Identify the function as a power function of the form 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 power rule formula.

4. Subtract 1 from the exponent: 3/2−1=3/2−2/2=1/2

5. Simplify the expression to its final form.

Final Answer

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

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