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

Problem

d()/d(x)*x(−1/2)

Solution

1. Identify the rule needed for the derivative, which is the Power Rule.

2. Apply the formula for the Power Rule, which states d(xn)/d(x)=n*x(n−1)

3. Substitute n=−1/2 into the formula.

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

5. Simplify the resulting expression.

Final Answer

d(x(−1/2))/d(x)=−1/2*x(−3/2)

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