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lnx^5
The derivative of the function/ lnx^5

Derivative of lnx^5

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

The graph:

from to

Piecewise:

The solution

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

  1. Let u=log⁡(x)u = \log{\left(x \right)}.

  2. Apply the power rule: u5u^{5} goes to 5u45 u^{4}

  3. Then, apply the chain rule. Multiply by ddxlog⁡(x)\frac{d}{d x} \log{\left(x \right)}:

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

    The result of the chain rule is:

    5log⁡(x)4x\frac{5 \log{\left(x \right)}^{4}}{x}

The answer is:

5log⁡(x)4x\frac{5 \log{\left(x \right)}^{4}}{x}

The graph
02468-8-6-4-2-1010-20002000
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
     4   
5*log (x)
---------
    x
5log⁡(x)4x\frac{5 \log{\left(x \right)}^{4}}{x}
Simplify
The second derivative [src] 
     3                
5*log (x)*(4 - log(x))
----------------------
           2          
          x
5⋅(−log⁡(x)+4)log⁡(x)3x2\frac{5 \cdot \left(- \log{\left(x \right)} + 4\right) \log{\left(x \right)}^{3}}{x^{2}}
Simplify
The third derivative [src] 
      2    /       2              \
10*log (x)*\6 + log (x) - 6*log(x)/
-----------------------------------
                  3                
                 x
10(log⁡(x)2−6log⁡(x)+6)log⁡(x)2x3\frac{10 \left(\log{\left(x \right)}^{2} - 6 \log{\left(x \right)} + 6\right) \log{\left(x \right)}^{2}}{x^{3}}
Simplify
The graph
Derivative of lnx^5
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