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

How to use it?
Derivative of:
Derivative of x^(-2)
Derivative of (x^2-1)^3
Derivative of sqrt(1/x)
Derivative of sin(x)^(9)
Identical expressions
(three *sqrt(three))/(two *x)
(3 multiply by square root of (3)) divide by (2 multiply by x)
(three multiply by square root of (three)) divide by (two multiply by x)
(3*√(3))/(2*x)
(3sqrt(3))/(2x)
3sqrt3/2x
(3*sqrt(3)) divide by (2*x)

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

Derivative of (3sqrt(3))/(2x)

The solution

You have entered [src]

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

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

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

Detail solution

The derivative of a constant times a function is the constant times the derivative of the function.
1. Let $u = 2 x$ .
2. Apply the power rule: $\frac{1}{u}$ goes to $- \frac{1}{u^{2}}$
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:
  
  $- \frac{1}{2 x^{2}}$
So, the result is: $- \frac{3 \sqrt{3}}{2 x^{2}}$

The answer is:

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

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

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

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

Simplify

The second derivative [src]

    ___
3*\/ 3 
-------
    3  
   x

$$\frac{3 \sqrt{3}}{x^{3}}$$

Simplify

The third derivative [src]

     ___
-9*\/ 3 
--------
    4   
   x

$$- \frac{9 \sqrt{3}}{x^{4}}$$

Simplify

The graph

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