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The derivative of the function/ f(x)=10logx/x

Derivative of f(x)=10logx/x

Function f() - derivative -N order at the point
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The graph:

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The solution

You have entered [src] 
10*log(x)
---------
    x
10log⁡(x)x\frac{10 \log{\left(x \right)}}{x} 
(10*log(x))/x
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)=10log⁡(x)f{\left(x \right)} = 10 \log{\left(x \right)} and g(x)=xg{\left(x \right)} = x.

    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: 10x\frac{10}{x}

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

    1. Apply the power rule: xx goes to 11

    Now plug in to the quotient rule:

    10−10log⁡(x)x2\frac{10 - 10 \log{\left(x \right)}}{x^{2}}

  2. Now simplify:

    10(1−log⁡(x))x2\frac{10 \left(1 - \log{\left(x \right)}\right)}{x^{2}}

The answer is:

10(1−log⁡(x))x2\frac{10 \left(1 - \log{\left(x \right)}\right)}{x^{2}}

The graph
02468-8-6-4-2-1010-50005000
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
10   10*log(x)
-- - ---------
 2        2   
x        x
−10log⁡(x)x2+10x2- \frac{10 \log{\left(x \right)}}{x^{2}} + \frac{10}{x^{2}}
Simplify
The second derivative [src] 
10*(-3 + 2*log(x))
------------------
         3        
        x
10(2log⁡(x)−3)x3\frac{10 \left(2 \log{\left(x \right)} - 3\right)}{x^{3}}
Simplify
The third derivative [src] 
10*(11 - 6*log(x))
------------------
         4        
        x
10(11−6log⁡(x))x4\frac{10 \left(11 - 6 \log{\left(x \right)}\right)}{x^{4}}
Simplify
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