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Derivative of:
Derivative of (5*x-6)*cos(x)-5*sin(x)-8
Derivative of 2/x²
Derivative of 2/(x+1)^2
Derivative of -2*cos(x)
Identical expressions
log^ two (x- five)
logarithm of squared (x minus 5)
logarithm of to the power of two (x minus five)
log2(x-5)
log2x-5
log²(x-5)
log to the power of 2(x-5)
log^2x-5
Similar expressions
log^2(x+5)

The derivative of the function/ log^2(x-5)

Derivative of log^2(x-5)

The solution

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   2       
log (x - 5)

$$\log{\left(x - 5 \right)}^{2}$$

log(x - 5)^2

Detail solution

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

$\frac{2 \log{\left(x - 5 \right)}}{x - 5}$
Now simplify:

$\frac{2 \log{\left(x - 5 \right)}}{x - 5}$

The answer is:

$\frac{2 \log{\left(x - 5 \right)}}{x - 5}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

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

$$\frac{2 \log{\left(x - 5 \right)}}{x - 5}$$

Simplify

The second derivative [src]

2*(1 - log(-5 + x))
-------------------
             2     
     (-5 + x)

$$\frac{2 \left(1 - \log{\left(x - 5 \right)}\right)}{\left(x - 5\right)^{2}}$$

Simplify

The third derivative [src]

2*(-3 + 2*log(-5 + x))
----------------------
              3       
      (-5 + x)

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

Simplify