Find the Derivative - d/dx f(x)=x^(5/2)

Problem

d(x(5/2))/d(x)

Solution

1. Identify the function as a power function of the form xn where n=5/2

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 5/2*x(5/2−1)

4. Simplify the exponent by calculating 5/2−2/2=3/2

Final Answer

d(x(5/2))/d(x)=5/2*x(3/2)

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