We have to find the derivative of log10 x
We define log functions as the inverses of exponentials:
y = ln(x) ⇔ x=ey
y=log10(x) ⇔ x=10y
Since we know how to differentiate exponentials, we can use implicit differentiation to find the derivatives of ln(x) and loga(x).
d/ dx [ln(x)] = 1/x
d/ dx [log10(x)]= 1/ x ln 10
The derivative of log10 x = 1/ x ln 10