Calculate the derivative of the function y = log(x) base 2.

The derivative of y = log(x) base 2 is 1/(xln2).

To find the derivative of y = log(x) base 2, we can use the formula for the derivative of a logarithmic function:

d/dx log_a(x) = 1/(xlna)

where a is the base of the logarithm. In this case, a = 2, so we have:

d/dx log_2(x) = 1/(xln2)

Therefore, the derivative of y = log(x) base 2 is:

dy/dx = d/dx log_2(x) = 1/(xln2)

We can simplify this expression by using the fact that ln2 is a constant:

dy/dx = 1/(xln2) = (1/ln2) * (1/x)

So the derivative of y = log(x) base 2 can also be written as:

dy/dx = (1/ln2) * (1/x)

This tells us that the rate of change of y with respect to x is proportional to 1/x, with a constant of proportionality equal to 1/ln2. As x gets larger, the rate of change of y gets smaller, but it never reaches zero. This is because the logarithmic function grows very slowly as x gets larger, but it never stops growing.