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(sqrt(2*x)-3)/6

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Derivative of:
Derivative of sqrt(x-1)/(sqrt(x^2-x)-1)
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Derivative of 4*sqrt(3)*x/3
Identical expressions
(sqrt(two *x)- three)/ six
( square root of (2 multiply by x) minus 3) divide by 6
( square root of (two multiply by x) minus three) divide by six
(√(2*x)-3)/6
(sqrt(2x)-3)/6
sqrt2x-3/6
(sqrt(2*x)-3) divide by 6
Similar expressions
(sqrt(2*x)+3)/6

The derivative of the function/ (sqrt(2*x)-3)/6

Derivative of (sqrt(2*x)-3)/6

The solution

You have entered [src]

  _____    
\/ 2*x  - 3
-----------
     6

$$\frac{\sqrt{2 x} - 3}{6}$$

  /  _____    \
d |\/ 2*x  - 3|
--|-----------|
dx\     6     /

$$\frac{d}{d x} \frac{\sqrt{2 x} - 3}{6}$$

Transform

Detail solution

The derivative of a constant times a function is the constant times the derivative of the function.
1. Differentiate $\sqrt{2 x} - 3$ term by term:
  1. Let $u = 2 x$ .
  2. Apply the power rule: $\sqrt{u}$ goes to $\frac{1}{2 \sqrt{u}}$
  3. Then, apply the chain rule. Multiply by $\frac{d}{d x} 2 x$ :
    1. 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: $2$
    The result of the chain rule is:
    
    $\frac{\sqrt{2}}{2 \sqrt{x}}$
  4. The derivative of the constant $\left(-1\right) 3$ is zero.
  The result is: $\frac{\sqrt{2}}{2 \sqrt{x}}$
So, the result is: $\frac{\sqrt{2}}{12 \sqrt{x}}$

The answer is:

$\frac{\sqrt{2}}{12 \sqrt{x}}$

The graph

Plot the graph f(x)

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The first derivative [src]

   ___  
 \/ 2   
--------
     ___
12*\/ x

$$\frac{\sqrt{2}}{12 \sqrt{x}}$$

Simplify

The second derivative [src]

   ___ 
-\/ 2  
-------
    3/2
24*x

$$- \frac{\sqrt{2}}{24 x^{\frac{3}{2}}}$$

Simplify

The third derivative [src]

   ___ 
 \/ 2  
-------
    5/2
16*x

$$\frac{\sqrt{2}}{16 x^{\frac{5}{2}}}$$

Simplify

The graph

Derivative of (sqrt(2*x)-3)/6