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

Problem

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

Solution

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

1/(2*x)=1/2*x(−1)

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

d()/d(x)1/2*x(−1)=1/2⋅(−1)*x(−1−1)

3. Simplify the resulting expression by performing the multiplication and subtracting the exponents.

−1/2*x(−2)

4. Convert the expression back into fraction form by moving the variable with the negative exponent to the denominator.

−1/(2*x2)

Final Answer

d()/d(x)1/(2*x)=−1/(2*x2)

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