Find the derivative of y = log_10(x)

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

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