Derivative of lnx^6

The solution

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   6   
log (x)

$$\log{\left(x \right)}^{6}$$

d /   6   \
--\log (x)/
dx

$$\frac{d}{d x} \log{\left(x \right)}^{6}$$

Transform

Detail solution

Let $u = \log{\left(x \right)}$ .
Apply the power rule: $u^{6}$ goes to $6 u^{5}$
Then, apply the chain rule. Multiply by $\frac{d}{d x} \log{\left(x \right)}$ :
1. The derivative of $\log{\left(x \right)}$ is $\frac{1}{x}$ .
The result of the chain rule is:

$\frac{6 \log{\left(x \right)}^{5}}{x}$

The answer is:

$\frac{6 \log{\left(x \right)}^{5}}{x}$

The first derivative [src]

     5   
6*log (x)
---------
    x

$$\frac{6 \log{\left(x \right)}^{5}}{x}$$

Simplify

The second derivative [src]

     4                
6*log (x)*(5 - log(x))
----------------------
           2          
          x

$$\frac{6 \cdot \left(5 - \log{\left(x \right)}\right) \log{\left(x \right)}^{4}}{x^{2}}$$

Simplify

The third derivative [src]

     3    /                      2   \
6*log (x)*\20 - 15*log(x) + 2*log (x)/
--------------------------------------
                   3                  
                  x

$$\frac{6 \cdot \left(2 \log{\left(x \right)}^{2} - 15 \log{\left(x \right)} + 20\right) \log{\left(x \right)}^{3}}{x^{3}}$$

Simplify

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Derivative of lnx^6

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