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Differentiate the function y = 1/(2x).

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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