Derivative of ln(5-2x^4)

You have entered [src]

   /       4\
log\5 - 2*x /

$$\log{\left(5 - 2 x^{4} \right)}$$

log(5 - 2*x^4)

Detail solution

Let $u = 5 - 2 x^{4}$ .
The derivative of $\log{\left(u \right)}$ is $\frac{1}{u}$ .
Then, apply the chain rule. Multiply by $\frac{d}{d x} \left(5 - 2 x^{4}\right)$ :
1. Differentiate $5 - 2 x^{4}$ term by term:
  1. The derivative of the constant $5$ 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: $x^{4}$ goes to $4 x^{3}$
    So, the result is: $- 8 x^{3}$
  The result is: $- 8 x^{3}$
The result of the chain rule is:

$- \frac{8 x^{3}}{5 - 2 x^{4}}$
Now simplify:

$\frac{8 x^{3}}{2 x^{4} - 5}$

The answer is:

$\frac{8 x^{3}}{2 x^{4} - 5}$

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

Other calculators

How to use it?

Identical expressions

Similar expressions

Derivative of ln(5-2x^4)

The graph:

Piecewise:

The solution