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y=log(2x^2-3x+6)

Derivative of y=log(2x^2-3x+6)

Function f() - derivative -N order at the point
v

The graph:

from to

Piecewise:

The solution

You have entered [src]
   /   2          \
log\2*x  - 3*x + 6/
$$\log{\left(\left(2 x^{2} - 3 x\right) + 6 \right)}$$
log(2*x^2 - 3*x + 6)
Detail solution
  1. Let .

  2. The derivative of is .

  3. Then, apply the chain rule. Multiply by :

    1. Differentiate term by term:

      1. Differentiate term by term:

        1. The derivative of a constant times a function is the constant times the derivative of the function.

          1. Apply the power rule: goes to

          So, the result is:

        2. The derivative of a constant times a function is the constant times the derivative of the function.

          1. Apply the power rule: goes to

          So, the result is:

        The result is:

      2. The derivative of the constant is zero.

      The result is:

    The result of the chain rule is:

  4. Now simplify:


The answer is:

The graph
The first derivative [src]
   -3 + 4*x   
--------------
   2          
2*x  - 3*x + 6
$$\frac{4 x - 3}{\left(2 x^{2} - 3 x\right) + 6}$$
The second derivative [src]
               2  
     (-3 + 4*x)   
4 - --------------
                 2
    6 - 3*x + 2*x 
------------------
               2  
  6 - 3*x + 2*x   
$$\frac{- \frac{\left(4 x - 3\right)^{2}}{2 x^{2} - 3 x + 6} + 4}{2 x^{2} - 3 x + 6}$$
The third derivative [src]
  /                2  \           
  |      (-3 + 4*x)   |           
2*|-6 + --------------|*(-3 + 4*x)
  |                  2|           
  \     6 - 3*x + 2*x /           
----------------------------------
                        2         
        /             2\          
        \6 - 3*x + 2*x /          
$$\frac{2 \left(4 x - 3\right) \left(\frac{\left(4 x - 3\right)^{2}}{2 x^{2} - 3 x + 6} - 6\right)}{\left(2 x^{2} - 3 x + 6\right)^{2}}$$
3-я производная [src]
  /                2  \           
  |      (-3 + 4*x)   |           
2*|-6 + --------------|*(-3 + 4*x)
  |                  2|           
  \     6 - 3*x + 2*x /           
----------------------------------
                        2         
        /             2\          
        \6 - 3*x + 2*x /          
$$\frac{2 \left(4 x - 3\right) \left(\frac{\left(4 x - 3\right)^{2}}{2 x^{2} - 3 x + 6} - 6\right)}{\left(2 x^{2} - 3 x + 6\right)^{2}}$$
The graph
Derivative of y=log(2x^2-3x+6)