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The derivative of the function/ ln(3x-4x^2)

Derivative of ln(3x-4x^2)

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

The graph:

from to

Piecewise:

The solution

You have entered [src] 
   /         2\
log\3*x - 4*x /
$$\log{\left(- 4 x^{2} + 3 x \right)}$$ 
log(3*x - 4*x^2)
Detail solution

  1. Let .

  2. The derivative of is .

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

    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:

    The result of the chain rule is:

  4. Now simplify:

The answer is:

The graph
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
 3 - 8*x  
----------
         2
3*x - 4*x
$$\frac{3 - 8 x}{- 4 x^{2} + 3 x}$$
Simplify
The second derivative [src] 
              2 
    (-3 + 8*x)  
8 - ------------
    x*(-3 + 4*x)
----------------
  x*(-3 + 4*x)
$$\frac{8 - \frac{\left(8 x - 3\right)^{2}}{x \left(4 x - 3\right)}}{x \left(4 x - 3\right)}$$
Simplify
The third derivative [src] 
  /                2 \           
  |      (-3 + 8*x)  |           
2*|-12 + ------------|*(-3 + 8*x)
  \      x*(-3 + 4*x)/           
---------------------------------
           2           2         
          x *(-3 + 4*x)
$$\frac{2 \left(-12 + \frac{\left(8 x - 3\right)^{2}}{x \left(4 x - 3\right)}\right) \left(8 x - 3\right)}{x^{2} \left(4 x - 3\right)^{2}}$$
Simplify
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