Calculate the derivative of the function y = log(x) base 10.

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

To find the derivative of y = log(x) base 10, we can use the formula for the derivative of a logarithmic function:

d/dx log_a(x) = 1/(xln(a))

where a is the base of the logarithm. In this case, a = 10, so we have:

d/dx log_10(x) = 1/(xln(10))

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

We can also check this result using the rules of logarithms. Recall that:

log_a(x) = log_b(x)/log_b(a)

where b is any base. In particular, we can write:

log_10(x) = ln(x)/ln(10)

Using this expression, we can rewrite y = log(x) base 10 as:

y = ln(x)/ln(10)

Taking the derivative of both sides with respect to x, we get:

dy/dx = (1/ln(10)) d/dx ln(x)

Using the chain rule, we have:

d/dx ln(x) = 1/x

Substituting this back into the previous equation, we get:

dy/dx = (1/ln(10)) (1/x)

Simplifying, we get:

dy/dx = 1/(xln(10))

which is the same result we obtained earlier.