Step-by-step Solution

Find the derivative of $\ln\left(5x\right)$

Go!
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Final Answer

$\frac{5}{5x}$

Step-by-step solution

Problem to solve:

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

Solving method

1

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 $\displaystyle f'(x)=\frac{a'}{a}$

$\frac{1}{5x}\frac{d}{dx}\left(5x\right)$
2

The derivative of the linear function times a constant, is equal to the constant

$\frac{5}{5x}$

Final Answer

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

Main topic:

Differential Calculus

Related Formulas:

3. See formulas

Time to solve it:

~ 0.04 s