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Derivative of:
Derivative of y=2x
Derivative of 5^(2*x)
Derivative of (1+tan(3*x)^(2))*e^(-x/2)
Derivative of (-x)/(x^2+1)
Identical expressions
sqrt((y- two)/ two)
square root of ((y minus 2) divide by 2)
square root of ((y minus two) divide by two)
√((y-2)/2)
sqrty-2/2
sqrt((y-2) divide by 2)
Similar expressions
sqrt((y+2)/2)

The derivative of the function/ sqrt((y-2)/2)

Derivative of sqrt((y-2)/2)

The solution

You have entered [src]

    _______
   / y - 2 
  /  ----- 
\/     2

$$\sqrt{\frac{y - 2}{2}}$$

sqrt((y - 2)/2)

Detail solution

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

$\frac{\sqrt{2}}{4 \sqrt{y - 2}}$
Now simplify:

$\frac{\sqrt{2}}{4 \sqrt{y - 2}}$

The answer is:

$\frac{\sqrt{2}}{4 \sqrt{y - 2}}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

/  ___   _______\
|\/ 2 *\/ y - 2 |
|---------------|
\       2       /
-----------------
    2*(y - 2)

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

Simplify

The second derivative [src]

      ___    
   -\/ 2     
-------------
          3/2
8*(-2 + y)

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

Simplify

The third derivative [src]

       ___    
   3*\/ 2     
--------------
           5/2
16*(-2 + y)

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

Simplify