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The derivative of the function/ sqrt(4-x)-2

Derivative of sqrt(4-x)-2

The solution

You have entered [src]

  _______    
\/ 4 - x  - 2

$$\sqrt{4 - x} - 2$$

sqrt(4 - x) - 2

Detail solution

Differentiate $\sqrt{4 - x} - 2$ term by term:
1. Let $u = 4 - x$ .
2. Apply the power rule: $\sqrt{u}$ goes to $\frac{1}{2 \sqrt{u}}$
3. Then, apply the chain rule. Multiply by $\frac{d}{d x} \left(4 - x\right)$ :
  1. Differentiate $4 - x$ term by term:
    1. The derivative of the constant $4$ 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: $x$ goes to $1$
      So, the result is: $-1$
    The result is: $-1$
  The result of the chain rule is:
  
  $- \frac{1}{2 \sqrt{4 - x}}$
4. The derivative of the constant $-2$ is zero.
The result is: $- \frac{1}{2 \sqrt{4 - x}}$

The answer is:

$- \frac{1}{2 \sqrt{4 - x}}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

    -1     
-----------
    _______
2*\/ 4 - x

$$- \frac{1}{2 \sqrt{4 - x}}$$

Simplify

The second derivative [src]

    -1      
------------
         3/2
4*(4 - x)

$$- \frac{1}{4 \left(4 - x\right)^{\frac{3}{2}}}$$

Simplify

The third derivative [src]

    -3      
------------
         5/2
8*(4 - x)

$$- \frac{3}{8 \left(4 - x\right)^{\frac{5}{2}}}$$

Simplify