Mister Exam

Lang:

Other calculators

How to use it?
Derivative of:
Derivative of (x+x^2)^x
Derivative of -sin(x)+cos(x)
Derivative of sin(x)-2*x
Derivative of f(x)=1/3x²+x²+2x
Identical expressions
log(one - two *x^ three)
logarithm of (1 minus 2 multiply by x cubed )
logarithm of (one minus two multiply by x to the power of three)
log(1-2*x3)
log1-2*x3
log(1-2*x³)
log(1-2*x to the power of 3)
log(1-2x^3)
log(1-2x3)
log1-2x3
log1-2x^3
Similar expressions
log(1+2*x^3)

The derivative of the function/ log(1-2*x^3)

Derivative of log(1-2*x^3)

The solution

You have entered [src]

   /       3\
log\1 - 2*x /

$$\log{\left(1 - 2 x^{3} \right)}$$

log(1 - 2*x^3)

Detail solution

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

$- \frac{6 x^{2}}{1 - 2 x^{3}}$
Now simplify:

$\frac{6 x^{2}}{2 x^{3} - 1}$

The answer is:

$\frac{6 x^{2}}{2 x^{3} - 1}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

     2  
 -6*x   
--------
       3
1 - 2*x

$$- \frac{6 x^{2}}{1 - 2 x^{3}}$$

Simplify

The second derivative [src]

     /          3  \
     |       3*x   |
12*x*|1 - ---------|
     |            3|
     \    -1 + 2*x /
--------------------
             3      
     -1 + 2*x

$$\frac{12 x \left(- \frac{3 x^{3}}{2 x^{3} - 1} + 1\right)}{2 x^{3} - 1}$$

Simplify

9-я производная [src]

       /             15             9            3            6               12             18 \
       |     629856*x        87480*x        324*x       9396*x        349920*x       419904*x   |
967680*|1 - ------------ - ------------ - --------- + ------------ + ------------ + ------------|
       |               5              3           3              2              4              6|
       |    /        3\    /        3\    -1 + 2*x    /        3\    /        3\    /        3\ |
       \    \-1 + 2*x /    \-1 + 2*x /                \-1 + 2*x /    \-1 + 2*x /    \-1 + 2*x / /
-------------------------------------------------------------------------------------------------
                                                      3                                          
                                           /        3\                                           
                                           \-1 + 2*x /

$$\frac{967680 \left(\frac{419904 x^{18}}{\left(2 x^{3} - 1\right)^{6}} - \frac{629856 x^{15}}{\left(2 x^{3} - 1\right)^{5}} + \frac{349920 x^{12}}{\left(2 x^{3} - 1\right)^{4}} - \frac{87480 x^{9}}{\left(2 x^{3} - 1\right)^{3}} + \frac{9396 x^{6}}{\left(2 x^{3} - 1\right)^{2}} - \frac{324 x^{3}}{2 x^{3} - 1} + 1\right)}{\left(2 x^{3} - 1\right)^{3}}$$

Simplify

The third derivative [src]

   /          3            6    \
   |      18*x         36*x     |
12*|1 - --------- + ------------|
   |            3              2|
   |    -1 + 2*x    /        3\ |
   \                \-1 + 2*x / /
---------------------------------
                    3            
            -1 + 2*x

$$\frac{12 \left(\frac{36 x^{6}}{\left(2 x^{3} - 1\right)^{2}} - \frac{18 x^{3}}{2 x^{3} - 1} + 1\right)}{2 x^{3} - 1}$$

Simplify

Other calculators

How to use it?

Identical expressions

Similar expressions

Derivative of log(1-2*x^3)

The graph:

Piecewise:

The solution