Find the Derivative - d/d@VAR f(x)=1/2x^2

Problem

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

Solution

1. Rewrite the expression using a negative exponent to prepare for the power rule.

1/(2*x2)=1/2*x(−2)

2. Apply the power rule for differentiation, 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 coefficient by multiplying 1/2 and −2

1/2⋅(−2)=−1

4. Simplify the exponent and rewrite the expression with a positive exponent.

−1*x(−3)=−1/(x3)

Final Answer

d()/d(x)1/(2*x2)=−1/(x3)

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