Mister Exam

Derivative of (x-3)*sqrt(x)

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

The graph:

from to

Piecewise:

The solution

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

    ; to find :

    1. Differentiate term by term:

      1. Apply the power rule: goes to

      2. The derivative of the constant is zero.

      The result 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]
  ___    x - 3 
\/ x  + -------
            ___
        2*\/ x 
$$\sqrt{x} + \frac{x - 3}{2 \sqrt{x}}$$
The second derivative [src]
    -3 + x
1 - ------
     4*x  
----------
    ___   
  \/ x    
$$\frac{1 - \frac{x - 3}{4 x}}{\sqrt{x}}$$
The third derivative [src]
  /     -3 + x\
3*|-2 + ------|
  \       x   /
---------------
        3/2    
     8*x       
$$\frac{3 \left(-2 + \frac{x - 3}{x}\right)}{8 x^{\frac{3}{2}}}$$
The graph
Derivative of (x-3)*sqrt(x)