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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
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The solution

You have entered [src] 
   /         2\
log\3*x - 4*x /
log⁡(−4x2+3x)\log{\left(- 4 x^{2} + 3 x \right)} 
log(3*x - 4*x^2)
Detail solution

  1. Let u=−4x2+3xu = - 4 x^{2} + 3 x.

  2. The derivative of log⁡(u)\log{\left(u \right)} is 1u\frac{1}{u}.

  3. Then, apply the chain rule. Multiply by ddx(−4x2+3x)\frac{d}{d x} \left(- 4 x^{2} + 3 x\right):

    1. Differentiate −4x2+3x- 4 x^{2} + 3 x 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: xx goes to 11

        So, the result is: 33

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

        1. Apply the power rule: x2x^{2} goes to 2x2 x

        So, the result is: −8x- 8 x

      The result is: 3−8x3 - 8 x

    The result of the chain rule is:

    3−8x−4x2+3x\frac{3 - 8 x}{- 4 x^{2} + 3 x}

  4. Now simplify:

    8x−3x(4x−3)\frac{8 x - 3}{x \left(4 x - 3\right)}

The answer is:

8x−3x(4x−3)\frac{8 x - 3}{x \left(4 x - 3\right)}

The graph
02468-8-6-4-2-1010-5050
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
 3 - 8*x  
----------
         2
3*x - 4*x
3−8x−4x2+3x\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)
8−(8x−3)2x(4x−3)x(4x−3)\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)
2(−12+(8x−3)2x(4x−3))(8x−3)x2(4x−3)2\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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