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

Derivative of sqrt(2x+3)

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

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  _________
\/ 2*x + 3
$$\sqrt{2 x + 3}$$ 
d /  _________\
--\\/ 2*x + 3 /
dx
$$\frac{d}{d x} \sqrt{2 x + 3}$$
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. 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] 
     1     
-----------
  _________
\/ 2*x + 3
$$\frac{1}{\sqrt{2 x + 3}}$$
Simplify
The second derivative [src] 
    -1      
------------
         3/2
(3 + 2*x)
$$- \frac{1}{\left(2 x + 3\right)^{\frac{3}{2}}}$$
Simplify
4-th derivative [src] 
    -15     
------------
         7/2
(3 + 2*x)
$$- \frac{15}{\left(2 x + 3\right)^{\frac{7}{2}}}$$
Simplify
The third derivative [src] 
     3      
------------
         5/2
(3 + 2*x)
$$\frac{3}{\left(2 x + 3\right)^{\frac{5}{2}}}$$
Simplify
The graph
Derivative of sqrt(2x+3)
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