Calculate the derivative of the function y = 10^2x.

The derivative of y = 10^2x is y' = 100ln(10)10^2x.

To find the derivative of y = 10^2x, we can use the power rule of differentiation. This states that if y = ax^n, then y' = anx^(n-1). Applying this rule to y = 10^2x, we get:

y' = 2(10^x)ln(10)

Since 10^x can be written as e^(xln(10)), we can substitute this into the equation to get:

y' = 2(e^(xln(10)))ln(10)

Using the chain rule of differentiation, we can simplify this to:

y' = 100ln(10)e^(xln(10))

Finally, we can substitute 10^x back into the equation to get:

y' = 100ln(10)10^2x

Therefore, the derivative of y = 10^2x is y' = 100ln(10)10^2x.