Derivative of log5(x)

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log(x)
------
log(5)

$$\frac{\log{\left(x \right)}}{\log{\left(5 \right)}}$$

log(x)/log(5)

Detail solution

The derivative of a constant times a function is the constant times the derivative of the function.
1. The derivative of $\log{\left(x \right)}$ is $\frac{1}{x}$ .
So, the result is: $\frac{1}{x \log{\left(5 \right)}}$

The answer is:

$\frac{1}{x \log{\left(5 \right)}}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

   1    
--------
x*log(5)

$$\frac{1}{x \log{\left(5 \right)}}$$

Simplify

The second derivative [src]

   -1    
---------
 2       
x *log(5)

$$- \frac{1}{x^{2} \log{\left(5 \right)}}$$

Simplify

The third derivative [src]

    2    
---------
 3       
x *log(5)

$$\frac{2}{x^{3} \log{\left(5 \right)}}$$

Simplify

The graph