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y=x(sqrtx^3)(sqrtx)

Derivative of y=x(sqrtx^3)(sqrtx)

Function f() - derivative -N order at the point
v

The graph:

from to

Piecewise:

The solution

You have entered [src]
       3      
    ___    ___
x*\/ x  *\/ x 
$$\sqrt{x} x \left(\sqrt{x}\right)^{3}$$
  /       3      \
d |    ___    ___|
--\x*\/ x  *\/ x /
dx                
$$\frac{d}{d x} \sqrt{x} x \left(\sqrt{x}\right)^{3}$$
Detail solution
  1. Apply the product rule:

    ; to find :

    1. Apply the power rule: goes to

    ; to find :

    1. Let .

    2. Apply the power rule: goes to

    3. Then, apply the chain rule. Multiply by :

      1. Apply the power rule: goes to

      The result of the chain rule is:

    ; to find :

    1. Apply the power rule: goes to

    The result is:

  2. Now simplify:


The answer is:

The graph
The first derivative [src]
   2       ___  3/2
3*x    3*\/ x *x   
---- + ------------
 2          2      
$$\frac{3 \sqrt{x} x^{\frac{3}{2}}}{2} + \frac{3 x^{2}}{2}$$
The second derivative [src]
6*x
$$6 x$$
The third derivative [src]
6
$$6$$
The graph
Derivative of y=x(sqrtx^3)(sqrtx)