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## Class 12 math (India)

### Course: Class 12 math (India)>Unit 5

Lesson 15: Logarithmic functions differentiation

# Differentiating logarithmic functions review

Review your logarithmic function differentiation skills and use them to solve problems.

## How do I differentiate logarithmic functions?

First, you should know the derivatives for the basic logarithmic functions:
$\frac{d}{dx}\mathrm{ln}\left(x\right)=\frac{1}{x}$
$\frac{d}{dx}{\mathrm{log}}_{b}\left(x\right)=\frac{1}{\mathrm{ln}\left(b\right)\cdot x}$
Notice that $\mathrm{ln}\left(x\right)={\mathrm{log}}_{e}\left(x\right)$ is a specific case of the general form ${\mathrm{log}}_{b}\left(x\right)$ where $b=e$. Since $\mathrm{ln}\left(e\right)=1$ we obtain the same result.
You can actually use the derivative of $\mathrm{ln}\left(x\right)$ (along with the constant multiple rule) to obtain the general derivative of ${\mathrm{log}}_{b}\left(x\right)$.

## Practice set 1: argument is $x$‍

Problem 1.1
$h\left(x\right)=7\mathrm{ln}\left(x\right)$
${h}^{\prime }\left(x\right)=?$
$g\left(x\right)=\mathrm{ln}\left(2{x}^{3}+1\right)$
${g}^{\prime }\left(x\right)=?$