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

Derivative of sqrt(x^3+2)

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

The graph:

from to

Piecewise:

The solution

You have entered [src] 
   ________
  /  3     
\/  x  + 2
$$\sqrt{x^{3} + 2}$$ 
  /   ________\
d |  /  3     |
--\\/  x  + 2 /
dx
$$\frac{d}{d x} \sqrt{x^{3} + 2}$$
Transform
Detail solution

  1. Let .

  2. Apply the power rule: goes to

  3. Then, apply the chain rule. Multiply by :

    1. Differentiate term by term:

      1. Apply the power rule: goes to

      2. The derivative of the constant is zero.

      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] 
        2    
     3*x     
-------------
     ________
    /  3     
2*\/  x  + 2
$$\frac{3 x^{2}}{2 \sqrt{x^{3} + 2}}$$
Simplify
The second derivative [src] 
    /          3   \
    |       3*x    |
3*x*|1 - ----------|
    |      /     3\|
    \    4*\2 + x //
--------------------
       ________     
      /      3      
    \/  2 + x
$$\frac{3 x \left(- \frac{3 x^{3}}{4 \left(x^{3} + 2\right)} + 1\right)}{\sqrt{x^{3} + 2}}$$
Simplify
The third derivative [src] 
  /          3             6   \
  |       9*x          27*x    |
3*|1 - ---------- + -----------|
  |      /     3\             2|
  |    2*\2 + x /     /     3\ |
  \                 8*\2 + x / /
--------------------------------
             ________           
            /      3            
          \/  2 + x
$$\frac{3 \cdot \left(\frac{27 x^{6}}{8 \left(x^{3} + 2\right)^{2}} - \frac{9 x^{3}}{2 \left(x^{3} + 2\right)} + 1\right)}{\sqrt{x^{3} + 2}}$$
Simplify
The graph
Derivative of sqrt(x^3+2)
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