differentiate. y = log 5x d/dx log 5x = □

Explanation:

Step1: Use change - of - base formula

We know that $\log_{a}x=\frac{\ln x}{\ln a}$. So, $y = \log_{5}x=\frac{\ln x}{\ln 5}$.

Step2: Differentiate using the constant - multiple rule

The derivative of a constant - multiple of a function $y = k\cdot f(x)$ (where $k$ is a constant and $f(x)$ is a function) is $y'=k\cdot f'(x)$. Here, $k = \frac{1}{\ln 5}$ and $f(x)=\ln x$. The derivative of $\ln x$ with respect to $x$ is $\frac{1}{x}$. So, $y'=\frac{1}{\ln 5}\cdot\frac{1}{x}$.

Answer:

$\frac{1}{x\ln 5}$