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Derivative of:
Derivative of 1/3*x^3
Derivative of x^2/(x^2+1)
Derivative of x^(5/2)
Derivative of (x+3)^2*(x+5)-1
Identical expressions
one /(sqrt(two)*x^ two)
1 divide by ( square root of (2) multiply by x squared )
one divide by ( square root of (two) multiply by x to the power of two)
1/(√(2)*x^2)
1/(sqrt(2)*x2)
1/sqrt2*x2
1/(sqrt(2)*x²)
1/(sqrt(2)*x to the power of 2)
1/(sqrt(2)x^2)
1/(sqrt(2)x2)
1/sqrt2x2
1/sqrt2x^2
1 divide by (sqrt(2)*x^2)

The derivative of the function/ 1/(sqrt(2)*x^2)

Derivative of 1/(sqrt(2)*x^2)

The solution

You have entered [src]

   1    
--------
  ___  2
\/ 2 *x

$$\frac{1}{\sqrt{2} x^{2}}$$

1/(sqrt(2)*x^2)

Detail solution

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

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

The answer is:

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

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

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

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

Simplify

The second derivative [src]

    ___
3*\/ 2 
-------
    4  
   x

$$\frac{3 \sqrt{2}}{x^{4}}$$

Simplify

The third derivative [src]

      ___
-12*\/ 2 
---------
     5   
    x

$$- \frac{12 \sqrt{2}}{x^{5}}$$

Simplify