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lnx^4
The derivative of the function/ lnx^4

Derivative of lnx^4

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

The graph:

from to

Piecewise:

The solution

You have entered [src] 
   4   
log (x)
log⁡(x)4\log{\left(x \right)}^{4} 
d /   4   \
--\log (x)/
dx
ddxlog⁡(x)4\frac{d}{d x} \log{\left(x \right)}^{4}
Transform
Detail solution

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

  2. Apply the power rule: u4u^{4} goes to 4u34 u^{3}

  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:

    4log⁡(x)3x\frac{4 \log{\left(x \right)}^{3}}{x}

The answer is:

4log⁡(x)3x\frac{4 \log{\left(x \right)}^{3}}{x}

The graph
02468-8-6-4-2-1010-500500
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
     3   
4*log (x)
---------
    x
4log⁡(x)3x\frac{4 \log{\left(x \right)}^{3}}{x}
Simplify
The second derivative [src] 
     2                
4*log (x)*(3 - log(x))
----------------------
           2          
          x
4⋅(−log⁡(x)+3)log⁡(x)2x2\frac{4 \cdot \left(- \log{\left(x \right)} + 3\right) \log{\left(x \right)}^{2}}{x^{2}}
Simplify
The third derivative [src] 
  /                    2   \       
4*\6 - 9*log(x) + 2*log (x)/*log(x)
-----------------------------------
                  3                
                 x
4⋅(2log⁡(x)2−9log⁡(x)+6)log⁡(x)x3\frac{4 \cdot \left(2 \log{\left(x \right)}^{2} - 9 \log{\left(x \right)} + 6\right) \log{\left(x \right)}}{x^{3}}
Simplify
The graph
Derivative of lnx^4
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