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Logarithmic differentiation Calculator

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1

Example

$\frac{d}{dx}\left(\ln\left(5x\right)\right)$
2

The derivative of the natural logarithm of a function is equal to the derivative of the function divided by that function. If $f(x)=ln\:a$ (where $a$ is a function of $x$), then $\displaystyle f'(x)=\frac{a'}{a}$

$\frac{1}{5x}\cdot\frac{d}{dx}\left(5x\right)$
3

The derivative of a function multiplied by a constant is equal to the constant times the derivative of the function

$5\frac{1}{5x}\cdot\frac{d}{dx}\left(x\right)$
4

The derivative of the linear function is equal to $1$

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

Multiply $5$ times $1$

$5\frac{1}{5x}$
6

Apply the formula: $a\frac{1}{x}$$=\frac{a}{x}$, where $a=5$ and $x=5x$

$\frac{5}{5x}$
7

Simplifying the fraction by $5$

$\frac{1}{x}$
8

Apply the formula: $\frac{1}{x}$$=x^{-1}$

$x^{-1}$
9

Applying the property of exponents, $\displaystyle a^{-n}=\frac{1}{a^n}$, where $n$ is a number

$\frac{1}{x}$