Question

What is the differentiation of$\log 2x$?

Answer 1

Differentiation of$\log 2x$.

Let $y=\log 2x$

Differentiate both sides, w.r.t $x$.

$$\begin{gathered} \frac{d}{dx}y=\frac{d}{dx}\log 2x \\ \Rightarrow \frac{dy}{dx}=\frac{1}{2x}\times \frac{d}{dx}\left(2x\right)\left[\begin{array}{c}chainrule:\frac{d}{dx}\left[f\left(g\left(x\right)\right)\right]=\frac{d}{dx}\left[f\left(g\left(x\right)\right)\right]\times \frac{d}{dx}g\left(x\right)\\ \because \frac{d}{dx}\log x=\frac{1}{x}\end{array}\right] \\ \Rightarrow \frac{dy}{dx}=\frac{1}{2x}\times 2 \\ \therefore \frac{dy}{dx}=\frac{1}{x} \end{gathered}$$

Thus, differentiation of$\log 2x$ is $\frac{1}{x}$.