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The derivative of y = log(2x) base 10 is 1/(xln10).

To find the derivative of y = log(2x) base 10, we can use the chain rule. Let u = 2x, then y = log(u) base 10. Using the chain rule, we have:

dy/dx = dy/du * du/dx

To find dy/du, we can use the formula for the derivative of log functions:

d/dx log_a(u) = 1/(u ln a)

In this case, a = 10, so we have:

dy/du = 1/(u ln 10)

Substituting back in for u, we have:

dy/dx = dy/du * du/dx

= 1/(u ln 10) * 2

= 2/(2x ln 10)

= 1/(x ln 10)

Therefore, the derivative of y = log(2x) base 10 is 1/(x ln 10).

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