Find the Derivative - d/dx 1/2x^(-1/2)

Problem

d()/d(x)1/2*x(−1/2)

Solution

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

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

3. Multiply the constant by the exponent: 1/2⋅(−1/2)=−1/4

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

5. Combine the results to form the final derivative.

Final Answer

d()/d(x)1/2*x(−1/2)=−1/4*x(−3/2)

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