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Identical expressions
log four (x^4-3x^ two)
logarithm of 4(x to the power of 4 minus 3x squared )
logarithm of four (x to the power of 4 minus 3x to the power of two)
log4(x4-3x2)
log4x4-3x2
log4(x⁴-3x²)
log4(x to the power of 4-3x to the power of 2)
log4x^4-3x^2
Similar expressions
log4(x^4+3x^2)

The derivative of the function/ log4(x^4-3x^2)

Derivative of log4(x^4-3x^2)

The solution

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

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

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

Detail solution

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

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

The answer is:

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

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

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

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

Simplify

The second derivative [src]

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

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

Simplify

The third derivative [src]

  /                 3                            \
  |      /        2\      /        2\ /        2\|
  |    4*\-3 + 2*x /    9*\-1 + 2*x /*\-3 + 2*x /|
4*|6 + -------------- - -------------------------|
  |                2            2 /      2\      |
  |     2 /      2\            x *\-3 + x /      |
  \    x *\-3 + x /                              /
--------------------------------------------------
                  /      2\                       
                x*\-3 + x /*log(4)

$$\frac{4 \left(6 - \frac{9 \left(2 x^{2} - 3\right) \left(2 x^{2} - 1\right)}{x^{2} \left(x^{2} - 3\right)} + \frac{4 \left(2 x^{2} - 3\right)^{3}}{x^{2} \left(x^{2} - 3\right)^{2}}\right)}{x \left(x^{2} - 3\right) \log{\left(4 \right)}}$$

Simplify

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Derivative of log4(x^4-3x^2)

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