Find the derivative of y = log_10(x)

We define log functions as the inverses of exponentials.

Answer: The derivative of log\(_{10}\)(x) = 1/ (x ln 10)

Let see, how we can find the derivative of y = log\(_{10}\)(x).

Explanation: 

We have to find the derivative of log₁₀ x

y = ln(x) ⇔ x=e^y

y = log\(_{10}\)(x) ⇔ x = 10^y

We will use the implicit differentiation to find the derivative of log\(_{a}\)(x).

d/dx [ln(x)] = 1/x

d/dx [log\(_{10}\)(x)] = 1 / (x ln 10). [Since log\(_{10}\)(x) = ln x/ln 10]

Thus, the derivative of log\(_{10}\)(x) = 1/ (x ln 10).