Mister Exam

Other calculators

sqrt(6-2x)
The derivative of the function/ sqrt(6-2x)

Derivative of sqrt(6-2x)

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

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  _________
\/ 6 - 2*x
$$\sqrt{6 - 2 x}$$ 
d /  _________\
--\\/ 6 - 2*x /
dx
$$\frac{d}{d x} \sqrt{6 - 2 x}$$
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 the constant is zero.

      2. The derivative of a constant times a function is the constant times the derivative of the function.

        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:

        So, the result is:

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