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y=ln5*log5(x)
The derivative of the function/ y=ln5*log5(x)

Derivative of y=ln5*log5(x)

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

The graph:

from to

Piecewise:

The solution

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

  1. Apply the quotient rule, which is:

    ddxf(x)g(x)=−f(x)ddxg(x)+g(x)ddxf(x)g2(x)\frac{d}{d x} \frac{f{\left(x \right)}}{g{\left(x \right)}} = \frac{- f{\left(x \right)} \frac{d}{d x} g{\left(x \right)} + g{\left(x \right)} \frac{d}{d x} f{\left(x \right)}}{g^{2}{\left(x \right)}}

    f(x)=log⁡(5)log⁡(x)f{\left(x \right)} = \log{\left(5 \right)} \log{\left(x \right)} and g(x)=log⁡(5)g{\left(x \right)} = \log{\left(5 \right)}.

    To find ddxf(x)\frac{d}{d x} f{\left(x \right)}:

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

      1. The derivative of log⁡(x)\log{\left(x \right)} is 1x\frac{1}{x}.

      So, the result is: log⁡(5)x\frac{\log{\left(5 \right)}}{x}

    To find ddxg(x)\frac{d}{d x} g{\left(x \right)}:

    1. The derivative of the constant log⁡(5)\log{\left(5 \right)} is zero.

    Now plug in to the quotient rule:

    1x\frac{1}{x}

The answer is:

1x\frac{1}{x}

The graph
02468-8-6-4-2-1010-2020
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
1
-
x
1x\frac{1}{x}
Simplify
The second derivative [src] 
-1 
---
  2
 x
−1x2- \frac{1}{x^{2}}
Simplify
3-th derivative [src] 
2 
--
 3
x
2x3\frac{2}{x^{3}}
Simplify
The third derivative [src] 
2 
--
 3
x
2x3\frac{2}{x^{3}}
Simplify
The graph
Derivative of y=ln5*log5(x)
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