How do you take the derivative of log base 10?

To find the derivative of the logarithm base 10, denoted as log10(x) or log(x), we start with the change of base formula. The derivative of log10(x) can be calculated using the natural logarithm.

Using the change of base formula, we can express the logarithm base 10 in terms of the natural logarithm:

log10(x) = &frac{log(x)}{log(10)} = &frac{ln(x)}{ln(10)}

Now we can differentiate it. Remember that ln(10) is just a constant. Using the quotient rule, we find:

&frac{d}{dx} log10(x) = &frac{1}{ln(10)} * &frac{d}{dx} ln(x) = &frac{1}{ln(10)} * &frac{1}{x}

Putting it all together, the derivative of log10(x) is:

&frac{d}{dx} log10(x) = &frac{1}{x * ln(10)}

This means that to take the derivative of log10(x), you simply take the derivative of the natural logarithm of x and divide it by ln(10).