Question

Find the derivative of $y={\log }_{10}\left(x\right)$.

Answer 1

Compute the derivative:

We know that $y=\ln \left(x\right)$ can be written as $x=e^y$.
That is we can write the given function $y={\log }_{10}\left(x\right)$ as $x={10}^y$.

Since,

$\frac{d}{dx}\left[\ln \right(x\left)\right]=\frac{1}{x}$

We can write that

$\frac{d}{dx}\left[{\log }_{10}\right(x\left)\right]=\frac{1}{x}\times \ln 10$

Hence, the derivative of $y={\log }_{10}\left(x\right)$ is $\frac{1}{x}\times \ln 10$.