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Derivative of:
Derivative of (x^5+1)
Derivative of x^sqrt(x)
Derivative of log(x+2)
Derivative of ex^2
Identical expressions
sqrt((five -x)/ two)
square root of ((5 minus x) divide by 2)
square root of ((five minus x) divide by two)
√((5-x)/2)
sqrt5-x/2
sqrt((5-x) divide by 2)
Similar expressions
sqrt((5+x)/2)

The derivative of the function/ sqrt((5-x)/2)

Derivative of sqrt((5-x)/2)

The solution

You have entered [src]

    _______
   / 5 - x 
  /  ----- 
\/     2

$$\sqrt{\frac{5 - x}{2}}$$

sqrt((5 - x)/2)

Detail solution

Let $u = \frac{5 - x}{2}$ .
Apply the power rule: $\sqrt{u}$ goes to $\frac{1}{2 \sqrt{u}}$
Then, apply the chain rule. Multiply by $\frac{d}{d x} \frac{5 - x}{2}$ :
1. The derivative of a constant times a function is the constant times the derivative of the function.
  1. Differentiate $5 - x$ term by term:
    1. The derivative of the constant $5$ 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: $-1$
  So, the result is: $- \frac{1}{2}$
The result of the chain rule is:

$- \frac{\sqrt{2}}{4 \sqrt{5 - x}}$

The answer is:

$- \frac{\sqrt{2}}{4 \sqrt{5 - x}}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

    ___   _______ 
  \/ 2 *\/ 5 - x  
- --------------- 
         2        
------------------
    2*(5 - x)

$$- \frac{\frac{1}{2} \sqrt{2} \sqrt{5 - x}}{2 \left(5 - x\right)}$$

Simplify

The second derivative [src]

     ___    
  -\/ 2     
------------
         3/2
8*(5 - x)

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

Simplify

The third derivative [src]

        ___  
   -3*\/ 2   
-------------
          5/2
16*(5 - x)

$$- \frac{3 \sqrt{2}}{16 \left(5 - x\right)^{\frac{5}{2}}}$$

Simplify