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Derivative of sin(x)^2
Derivative of (x^2+3x)(2x-4)
Derivative of log(x^2-6x+10)
Derivative of 9*sin^2(3*x)*cos(3*x)
Graphing y =:
log(x^2-6x+10)
Identical expressions
log(x^ two -6x+ ten)
logarithm of (x squared minus 6x plus 10)
logarithm of (x to the power of two minus 6x plus ten)
log(x2-6x+10)
logx2-6x+10
log(x²-6x+10)
log(x to the power of 2-6x+10)
logx^2-6x+10
Similar expressions
log(x^2+6x+10)
log(x^2-6x-10)

The derivative of the function/ log(x^2-6x+10)

Derivative of log(x^2-6x+10)

The solution

You have entered [src]

   / 2           \
log\x  - 6*x + 10/

$$\log{\left(\left(x^{2} - 6 x\right) + 10 \right)}$$

log(x^2 - 6*x + 10)

Detail solution

Let $u = \left(x^{2} - 6 x\right) + 10$ .
The derivative of $\log{\left(u \right)}$ is $\frac{1}{u}$ .
Then, apply the chain rule. Multiply by $\frac{d}{d x} \left(\left(x^{2} - 6 x\right) + 10\right)$ :
1. Differentiate $\left(x^{2} - 6 x\right) + 10$ term by term:
  1. Differentiate $x^{2} - 6 x$ 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. Apply the power rule: $x$ goes to $1$
      So, the result is: $-6$
    The result is: $2 x - 6$
  2. The derivative of the constant $10$ is zero.
  The result is: $2 x - 6$
The result of the chain rule is:

$\frac{2 x - 6}{\left(x^{2} - 6 x\right) + 10}$
Now simplify:

$\frac{2 \left(x - 3\right)}{x^{2} - 6 x + 10}$

The answer is:

$\frac{2 \left(x - 3\right)}{x^{2} - 6 x + 10}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

   -6 + 2*x  
-------------
 2           
x  - 6*x + 10

$$\frac{2 x - 6}{\left(x^{2} - 6 x\right) + 10}$$

Simplify

The second derivative [src]

  /               2 \
  |     2*(-3 + x)  |
2*|1 - -------------|
  |          2      |
  \    10 + x  - 6*x/
---------------------
          2          
    10 + x  - 6*x

$$\frac{2 \left(- \frac{2 \left(x - 3\right)^{2}}{x^{2} - 6 x + 10} + 1\right)}{x^{2} - 6 x + 10}$$

Simplify

The third derivative [src]

           /                2 \
           |      4*(-3 + x)  |
4*(-3 + x)*|-3 + -------------|
           |           2      |
           \     10 + x  - 6*x/
-------------------------------
                       2       
        /      2      \        
        \10 + x  - 6*x/

$$\frac{4 \left(x - 3\right) \left(\frac{4 \left(x - 3\right)^{2}}{x^{2} - 6 x + 10} - 3\right)}{\left(x^{2} - 6 x + 10\right)^{2}}$$

Simplify

The graph

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Derivative of log(x^2-6x+10)

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The solution