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1/(3*sqrt(x+1))

Derivative of 1/(3*sqrt(x+1))

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

The graph:

from to

Piecewise:

The solution

You have entered [src]
     1     
-----------
    _______
3*\/ x + 1 
$$\frac{1}{3 \sqrt{x + 1}}$$
1/(3*sqrt(x + 1))
Detail solution
  1. Let .

  2. Apply the power rule: goes to

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

    1. The derivative of a constant times a function is the constant times the derivative of the function.

      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:

      So, the result is:

    The result of the chain rule is:

  4. Now simplify:


The answer is:

The graph
The first derivative [src]
       1      
- ----------- 
      _______ 
  3*\/ x + 1  
--------------
  2*(x + 1)   
$$- \frac{\frac{1}{3} \frac{1}{\sqrt{x + 1}}}{2 \left(x + 1\right)}$$
The second derivative [src]
     1      
------------
         5/2
4*(1 + x)   
$$\frac{1}{4 \left(x + 1\right)^{\frac{5}{2}}}$$
The third derivative [src]
    -5      
------------
         7/2
8*(1 + x)   
$$- \frac{5}{8 \left(x + 1\right)^{\frac{7}{2}}}$$
The graph
Derivative of 1/(3*sqrt(x+1))