Mister Exam

Lang:

Other calculators

How to use it?
Derivative of:
Derivative of x^3+1/x-1
Derivative of x^2/cosx
Derivative of sin(x-(3/5))-(8/5)
Derivative of e^x/(1+x^2)
Identical expressions
ln(two +(x^ three))
ln(2 plus (x cubed ))
ln(two plus (x to the power of three))
ln(2+(x3))
ln2+x3
ln(2+(x³))
ln(2+(x to the power of 3))
ln2+x^3
Similar expressions
ln(2-(x^3))

The derivative of the function/ ln(2+(x^3))

Derivative of ln(2+(x^3))

The solution

You have entered [src]

   /     3\
log\2 + x /

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

log(2 + x^3)

Detail solution

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

$\frac{3 x^{2}}{x^{3} + 2}$

The answer is:

$\frac{3 x^{2}}{x^{3} + 2}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

    2 
 3*x  
------
     3
2 + x

$$\frac{3 x^{2}}{x^{3} + 2}$$

Simplify

The second derivative [src]

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

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

Simplify

The third derivative [src]

  /        3          6  \
  |     9*x        9*x   |
6*|1 - ------ + ---------|
  |         3           2|
  |    2 + x    /     3\ |
  \             \2 + x / /
--------------------------
               3          
          2 + x

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

Simplify

Other calculators

How to use it?

Identical expressions

Similar expressions

Derivative of ln(2+(x^3))

The graph:

Piecewise:

The solution