Mister Exam

Derivative of sqrt(2x+5)

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

The graph:

from to

Enter:

The solution

You have entered [src]
  _________
\/ 2*x + 5 
$$\sqrt{2 x + 5}$$
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 answer is:

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
Derivative of sqrt(2x+5)
    To see a detailed solution - share to all your student friends
    To see a detailed solution,
    share to all your student friends: