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sqrt(4*x+1)

Derivative of sqrt(4*x+1)

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

The graph:

from to

Piecewise:

The solution

You have entered [src]
  _________
\/ 4*x + 1 
$$\sqrt{4 x + 1}$$
sqrt(4*x + 1)
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
The first derivative [src]
     2     
-----------
  _________
\/ 4*x + 1 
$$\frac{2}{\sqrt{4 x + 1}}$$
The second derivative [src]
    -4      
------------
         3/2
(1 + 4*x)   
$$- \frac{4}{\left(4 x + 1\right)^{\frac{3}{2}}}$$
The third derivative [src]
     24     
------------
         5/2
(1 + 4*x)   
$$\frac{24}{\left(4 x + 1\right)^{\frac{5}{2}}}$$
The graph
Derivative of sqrt(4*x+1)