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

Problem

d()/d(x)1/(2*x2)

Solution

1. Rewrite the expression using a negative exponent to make it easier to differentiate.

1/(2*x2)=1/2*x(−2)

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

d()/d(x)1/2*x(−2)=1/2⋅(−2)*x(−2−1)

3. Simplify the coefficients and the exponent.

1/2⋅(−2)=−1

−1*x(−3)=−x(−3)

4. Rewrite the result with a positive exponent by moving the variable back to the denominator.

−x(−3)=−1/(x3)

Final Answer

d()/d(x)1/(2*x2)=−1/(x3)

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