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Identical expressions
f(x)=log two (4x-3x^2)
f(x) equally logarithm of 2(4x minus 3x squared )
f(x) equally logarithm of two (4x minus 3x squared )
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Similar expressions
f(x)=log2(4x+3x^2)

The derivative of the function/ f(x)=log2(4x-3x^2)

Derivative of f(x)=log2(4x-3x^2)

The solution

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   /         2\
log\4*x - 3*x /
---------------
     log(2)

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

log(4*x - 3*x^2)/log(2)

Detail solution

The derivative of a constant times a function is the constant times the derivative of the function.
1. Let $u = - 3 x^{2} + 4 x$ .
2. The derivative of $\log{\left(u \right)}$ is $\frac{1}{u}$ .
3. Then, apply the chain rule. Multiply by $\frac{d}{d x} \left(- 3 x^{2} + 4 x\right)$ :
  1. Differentiate $- 3 x^{2} + 4 x$ 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: $x$ goes to $1$
      So, the result is: $4$
    2. The derivative of a constant times a function is the constant times the derivative of the function.
      1. Apply the power rule: $x^{2}$ goes to $2 x$
      So, the result is: $- 6 x$
    The result is: $4 - 6 x$
  The result of the chain rule is:
  
  $\frac{4 - 6 x}{- 3 x^{2} + 4 x}$
So, the result is: $\frac{4 - 6 x}{\left(- 3 x^{2} + 4 x\right) \log{\left(2 \right)}}$
Now simplify:

$\frac{2 \left(3 x - 2\right)}{x \left(3 x - 4\right) \log{\left(2 \right)}}$

The answer is:

$\frac{2 \left(3 x - 2\right)}{x \left(3 x - 4\right) \log{\left(2 \right)}}$

The graph

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The first derivative [src]

      4 - 6*x      
-------------------
/         2\       
\4*x - 3*x /*log(2)

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

Simplify

The second derivative [src]

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

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

Simplify

The third derivative [src]

              /                2\
              |    4*(-2 + 3*x) |
-4*(-2 + 3*x)*|9 - -------------|
              \     x*(-4 + 3*x)/
---------------------------------
       2           2             
      x *(-4 + 3*x) *log(2)

$$- \frac{4 \left(9 - \frac{4 \left(3 x - 2\right)^{2}}{x \left(3 x - 4\right)}\right) \left(3 x - 2\right)}{x^{2} \left(3 x - 4\right)^{2} \log{\left(2 \right)}}$$

Simplify

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Derivative of f(x)=log2(4x-3x^2)

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