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Derivative of:
Derivative of 1/tg(x)
Derivative of (1-x^2)^2
Derivative of y=x^3-8x^2+10x-4
Derivative of x/(x^2+4)
Integral of d{x}:
x^2/sqrt(x)
Identical expressions
x^ two /sqrt(x)
x squared divide by square root of (x)
x to the power of two divide by square root of (x)
x^2/√(x)
x2/sqrt(x)
x2/sqrtx
x²/sqrt(x)
x to the power of 2/sqrt(x)
x^2/sqrtx
x^2 divide by sqrt(x)

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

Derivative of x^2/sqrt(x)

The solution

You have entered [src]

   2 
  x  
-----
  ___
\/ x

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

x^2/sqrt(x)

Detail solution

Apply the quotient rule, which is:

$\frac{d}{d x} \frac{f{\left(x \right)}}{g{\left(x \right)}} = \frac{- f{\left(x \right)} \frac{d}{d x} g{\left(x \right)} + g{\left(x \right)} \frac{d}{d x} f{\left(x \right)}}{g^{2}{\left(x \right)}}$

$f{\left(x \right)} = x^{2}$ and $g{\left(x \right)} = \sqrt{x}$ .

To find $\frac{d}{d x} f{\left(x \right)}$ :
1. Apply the power rule: $x^{2}$ goes to $2 x$
To find $\frac{d}{d x} g{\left(x \right)}$ :
1. Apply the power rule: $\sqrt{x}$ goes to $\frac{1}{2 \sqrt{x}}$
Now plug in to the quotient rule:

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

The answer is:

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

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

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

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

Simplify

The second derivative [src]

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

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

Simplify

The third derivative [src]

 -3   
------
   3/2
8*x

$$- \frac{3}{8 x^{\frac{3}{2}}}$$

Simplify

The graph

Derivative of x^2/sqrt(x)