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Identical expressions
log(x- four , eight)^ five
logarithm of (x minus 4,8) to the power of 5
logarithm of (x minus four , eight) to the power of five
log(x-4,8)5
logx-4,85
log(x-4,8)⁵
logx-4,8^5
Similar expressions
log(x+4,8)^5

The derivative of the function/ log(x-4,8)^5

Derivative of log(x-4,8)^5

The solution

You have entered [src]

   5          
log (x - 24/5)

$$\log{\left(x - \frac{24}{5} \right)}^{5}$$

log(x - 24/5)^5

Detail solution

Let $u = \log{\left(x - \frac{24}{5} \right)}$ .
Apply the power rule: $u^{5}$ goes to $5 u^{4}$
Then, apply the chain rule. Multiply by $\frac{d}{d x} \log{\left(x - \frac{24}{5} \right)}$ :
1. Let $u = x - \frac{24}{5}$ .
2. The derivative of $\log{\left(u \right)}$ is $\frac{1}{u}$ .
3. Then, apply the chain rule. Multiply by $\frac{d}{d x} \left(x - \frac{24}{5}\right)$ :
  1. Differentiate $x - \frac{24}{5}$ term by term:
    1. Apply the power rule: $x$ goes to $1$
    2. The derivative of the constant $- \frac{24}{5}$ is zero.
    The result is: $1$
  The result of the chain rule is:
  
  $\frac{1}{x - \frac{24}{5}}$
The result of the chain rule is:

$\frac{5 \log{\left(x - \frac{24}{5} \right)}^{4}}{x - \frac{24}{5}}$
Now simplify:

$\frac{25 \log{\left(x - \frac{24}{5} \right)}^{4}}{5 x - 24}$

The answer is:

$\frac{25 \log{\left(x - \frac{24}{5} \right)}^{4}}{5 x - 24}$

The graph

Plot the graph f(x)

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The first derivative [src]

     4          
5*log (x - 24/5)
----------------
    x - 24/5

$$\frac{5 \log{\left(x - \frac{24}{5} \right)}^{4}}{x - \frac{24}{5}}$$

Simplify

The second derivative [src]

       3                                
125*log (-24/5 + x)*(4 - log(-24/5 + x))
----------------------------------------
                         2              
              (-24 + 5*x)

$$\frac{125 \left(4 - \log{\left(x - \frac{24}{5} \right)}\right) \log{\left(x - \frac{24}{5} \right)}^{3}}{\left(5 x - 24\right)^{2}}$$

Simplify

The third derivative [src]

        2            /       2                              \
1250*log (-24/5 + x)*\6 + log (-24/5 + x) - 6*log(-24/5 + x)/
-------------------------------------------------------------
                                    3                        
                         (-24 + 5*x)

$$\frac{1250 \left(\log{\left(x - \frac{24}{5} \right)}^{2} - 6 \log{\left(x - \frac{24}{5} \right)} + 6\right) \log{\left(x - \frac{24}{5} \right)}^{2}}{\left(5 x - 24\right)^{3}}$$

Simplify

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Derivative of log(x-4,8)^5

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The solution