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The derivative of the function/ ln(5-2x^4)

Derivative of ln(5-2x^4)

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

The graph:

from to

Piecewise:

The solution

You have entered [src] 
   /       4\
log\5 - 2*x /
$$\log{\left(5 - 2 x^{4} \right)}$$ 
log(5 - 2*x^4)
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 the constant is zero.

      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   
--------
       4
5 - 2*x
$$- \frac{8 x^{3}}{5 - 2 x^{4}}$$
Simplify
The second derivative [src] 
     /          4  \
   2 |       8*x   |
8*x *|3 - ---------|
     |            4|
     \    -5 + 2*x /
--------------------
             4      
     -5 + 2*x
$$\frac{8 x^{2} \left(- \frac{8 x^{4}}{2 x^{4} - 5} + 3\right)}{2 x^{4} - 5}$$
Simplify
The third derivative [src] 
     /          4            8    \
     |      36*x         64*x     |
16*x*|3 - --------- + ------------|
     |            4              2|
     |    -5 + 2*x    /        4\ |
     \                \-5 + 2*x / /
-----------------------------------
                     4             
             -5 + 2*x
$$\frac{16 x \left(\frac{64 x^{8}}{\left(2 x^{4} - 5\right)^{2}} - \frac{36 x^{4}}{2 x^{4} - 5} + 3\right)}{2 x^{4} - 5}$$
Simplify
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