Mister Exam

Derivative of sqrt(2x+6)-x

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

The graph:

from to

Piecewise:

The solution

You have entered [src]
  _________    
\/ 2*x + 6  - x
$$- x + \sqrt{2 x + 6}$$
sqrt(2*x + 6) - x
Detail solution
  1. Differentiate term by term:

    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. 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:

    The result is:

  2. Now simplify:


The answer is:

The graph
The first derivative [src]
          1     
-1 + -----------
       _________
     \/ 2*x + 6 
$$-1 + \frac{1}{\sqrt{2 x + 6}}$$
The second derivative [src]
     ___    
  -\/ 2     
------------
         3/2
4*(3 + x)   
$$- \frac{\sqrt{2}}{4 \left(x + 3\right)^{\frac{3}{2}}}$$
The third derivative [src]
      ___   
  3*\/ 2    
------------
         5/2
8*(3 + x)   
$$\frac{3 \sqrt{2}}{8 \left(x + 3\right)^{\frac{5}{2}}}$$
The graph
Derivative of sqrt(2x+6)-x