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sqrt(4-x)
The derivative of the function/ sqrt(4-x)

Derivative of sqrt(4-x)

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

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  _______
\/ 4 - x
$$\sqrt{- x + 4}$$ 
d /  _______\
--\\/ 4 - x /
dx
$$\frac{d}{d x} \sqrt{- x + 4}$$
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. Apply the power rule: goes to

        So, the result is:

      The result is:

    The result of the chain rule is:

The answer is:

The graph
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
    -1     
-----------
    _______
2*\/ 4 - x
$$- \frac{1}{2 \sqrt{- x + 4}}$$
Simplify
The second derivative [src] 
    -1      
------------
         3/2
4*(4 - x)
$$- \frac{1}{4 \left(- x + 4\right)^{\frac{3}{2}}}$$
Simplify
The third derivative [src] 
    -3      
------------
         5/2
8*(4 - x)
$$- \frac{3}{8 \left(- x + 4\right)^{\frac{5}{2}}}$$
Simplify
The graph
Derivative of sqrt(4-x)
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