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Derivative of (x-2)^2
Derivative of 2*x^2
Derivative of 4^x
Derivative of x*x
Identical expressions
y=log seven (x^ two -8x+7)
y equally logarithm of 7(x squared minus 8x plus 7)
y equally logarithm of seven (x to the power of two minus 8x plus 7)
y=log7(x2-8x+7)
y=log7x2-8x+7
y=log7(x²-8x+7)
y=log7(x to the power of 2-8x+7)
y=log7x^2-8x+7
Similar expressions
y=log7(x^2+8x+7)
y=log7(x^2-8x-7)

The derivative of the function/ y=log7(x^2-8x+7)

Derivative of y=log7(x^2-8x+7)

The solution

You have entered [src]

   / 2          \
log\x  - 8*x + 7/
-----------------
      log(7)

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

  /   / 2          \\
d |log\x  - 8*x + 7/|
--|-----------------|
dx\      log(7)     /

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

Transform

Detail solution

The derivative of a constant times a function is the constant times the derivative of the function.
1. Let $u = x^{2} - 8 x + 7$ .
2. The derivative of $\log{\left(u \right)}$ is $\frac{1}{u}$ .
3. Then, apply the chain rule. Multiply by $\frac{d}{d x} \left(x^{2} - 8 x + 7\right)$ :
  1. Differentiate $x^{2} - 8 x + 7$ term by term:
    1. Apply the power rule: $x^{2}$ goes to $2 x$
    2. The derivative of a constant times a function is the constant times the derivative of the function.
      1. The derivative of a constant times a function is the constant times the derivative of the function.
        
        Apply the power rule: $x$ goes to $1$
        
        So, the result is: $8$
      So, the result is: $-8$
    3. The derivative of the constant $7$ is zero.
    The result is: $2 x - 8$
  The result of the chain rule is:
  
  $\frac{2 x - 8}{x^{2} - 8 x + 7}$
So, the result is: $\frac{2 x - 8}{\left(x^{2} - 8 x + 7\right) \log{\left(7 \right)}}$
Now simplify:

$\frac{2 \left(x - 4\right)}{\left(x^{2} - 8 x + 7\right) \log{\left(7 \right)}}$

The answer is:

$\frac{2 \left(x - 4\right)}{\left(x^{2} - 8 x + 7\right) \log{\left(7 \right)}}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

       -8 + 2*x      
---------------------
/ 2          \       
\x  - 8*x + 7/*log(7)

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

Simplify

The second derivative [src]

   /               2 \
   |     2*(-4 + x)  |
-2*|-1 + ------------|
   |          2      |
   \     7 + x  - 8*x/
----------------------
/     2      \        
\7 + x  - 8*x/*log(7)

$$- \frac{2 \cdot \left(\frac{2 \left(x - 4\right)^{2}}{x^{2} - 8 x + 7} - 1\right)}{\left(x^{2} - 8 x + 7\right) \log{\left(7 \right)}}$$

Simplify

The third derivative [src]

           /               2 \
           |     4*(-4 + x)  |
4*(-4 + x)*|-3 + ------------|
           |          2      |
           \     7 + x  - 8*x/
------------------------------
                  2           
    /     2      \            
    \7 + x  - 8*x/ *log(7)

$$\frac{4 \left(x - 4\right) \left(\frac{4 \left(x - 4\right)^{2}}{x^{2} - 8 x + 7} - 3\right)}{\left(x^{2} - 8 x + 7\right)^{2} \log{\left(7 \right)}}$$

Simplify

The graph

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Derivative of y=log7(x^2-8x+7)

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