# Derivative of sqrt(2x+5)

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

from to

### The solution

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