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log5(3x)
The derivative of the function/ log5(3x)

Derivative of log5(3x)

Function f() - derivative -N order at the point
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
log(3*x)
--------
 log(5)
$$\frac{\log{\left(3 x \right)}}{\log{\left(5 \right)}}$$ 
d /log(3*x)\
--|--------|
dx\ log(5) /
$$\frac{d}{d x} \frac{\log{\left(3 x \right)}}{\log{\left(5 \right)}}$$
Transform
Detail solution

  1. The derivative of a constant times a function is the constant times the derivative of the function.

    1. Let .

    2. The derivative of is .

    3. Then, apply the chain rule. Multiply by :

      1. The derivative of a constant times a function is the constant times the derivative of the function.

        1. Apply the power rule: goes to

        So, the result is:

      The result of the chain rule is:

    So, the result is:

The answer is:

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
Derivative of log5(3x)
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