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The derivative of y = 1/(2x) is -1/(2x^2).

To differentiate the function y = 1/(2x), we can use the power rule of differentiation. This rule states that if y = x^n, then dy/dx = nx^(n-1). In this case, we can rewrite y as y = (1/2)x^(-1). Applying the power rule, we get:

dy/dx = (-1/2)x^(-2)

Simplifying this expression, we get:

dy/dx = -1/(2x^2)

Therefore, the derivative of y = 1/(2x) is -1/(2x^2). This means that the slope of the tangent line to the graph of y at any point (x,y) is given by -1/(2x^2). We can use this derivative to find the `equation of the tangent line`

at a specific point, or to analyse the behaviour of the function near certain values of x. For example, as x approaches 0, the derivative becomes very large in magnitude, indicating that the function has a vertical asymptote at x = 0. For a more detailed exploration of different types of functions and their properties, you can read more on `types of numbers`

. If you're looking to expand your understanding of derivatives, consider exploring `advanced differentiation techniques`

. To get a foundational understanding of derivatives, visit `introduction to derivatives.`

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