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The derivative of the function/ sqrt(3x^2+5)

Derivative of sqrt(3x^2+5)

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

The graph:

from to

Piecewise:

The solution

You have entered [src] 
   __________
  /    2     
\/  3*x  + 5
$$\sqrt{3 x^{2} + 5}$$ 
sqrt(3*x^2 + 5)
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. The derivative of a constant times a function is the constant times the derivative of the function.

        1. Apply the power rule: goes to

        So, the result is:

      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] 
     3*x     
-------------
   __________
  /    2     
\/  3*x  + 5
$$\frac{3 x}{\sqrt{3 x^{2} + 5}}$$
Simplify
The second derivative [src] 
  /         2  \
  |      3*x   |
3*|1 - --------|
  |           2|
  \    5 + 3*x /
----------------
    __________  
   /        2   
 \/  5 + 3*x
$$\frac{3 \left(- \frac{3 x^{2}}{3 x^{2} + 5} + 1\right)}{\sqrt{3 x^{2} + 5}}$$
Simplify
The third derivative [src] 
     /          2  \
     |       3*x   |
27*x*|-1 + --------|
     |            2|
     \     5 + 3*x /
--------------------
             3/2    
   /       2\       
   \5 + 3*x /
$$\frac{27 x \left(\frac{3 x^{2}}{3 x^{2} + 5} - 1\right)}{\left(3 x^{2} + 5\right)^{\frac{3}{2}}}$$
Simplify
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