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Derivative of tanx
Derivative of (x+3)^2(x+5)-1
Derivative of sin2x+cos2x
Derivative of log(x)^(3)^2
Identical expressions
log(x)^(three)^ two
logarithm of (x) to the power of (3) squared
logarithm of (x) to the power of (three) to the power of two
log(x)(3)2
logx32
log(x)^(3)²
log(x) to the power of (3) to the power of 2
logx^3^2

The derivative of the function/ log(x)^(3)^2

Derivative of log(x)^(3)^2

The solution

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   9   
log (x)

$$\log{\left(x \right)}^{9}$$

log(x)^9

Detail solution

Let $u = \log{\left(x \right)}$ .
Apply the power rule: $u^{9}$ goes to $9 u^{8}$
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:

$\frac{9 \log{\left(x \right)}^{8}}{x}$

The answer is:

$\frac{9 \log{\left(x \right)}^{8}}{x}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

     8   
9*log (x)
---------
    x

$$\frac{9 \log{\left(x \right)}^{8}}{x}$$

Simplify

The second derivative [src]

     7                
9*log (x)*(8 - log(x))
----------------------
           2          
          x

$$\frac{9 \left(8 - \log{\left(x \right)}\right) \log{\left(x \right)}^{7}}{x^{2}}$$

Simplify

The third derivative [src]

      6    /        2               \
18*log (x)*\28 + log (x) - 12*log(x)/
-------------------------------------
                   3                 
                  x

$$\frac{18 \left(\log{\left(x \right)}^{2} - 12 \log{\left(x \right)} + 28\right) \log{\left(x \right)}^{6}}{x^{3}}$$

Simplify

The graph

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Derivative of log(x)^(3)^2

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The solution