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(x^3+4)/(x^2)

Derivative of (x^3+4)/(x^2)

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

The graph:

from to

Piecewise:

The solution

You have entered [src]
 3    
x  + 4
------
   2  
  x   
$$\frac{x^{3} + 4}{x^{2}}$$
  / 3    \
d |x  + 4|
--|------|
dx|   2  |
  \  x   /
$$\frac{d}{d x} \frac{x^{3} + 4}{x^{2}}$$
Detail solution
  1. Apply the quotient rule, which is:

    and .

    To find :

    1. Differentiate term by term:

      1. The derivative of the constant is zero.

      2. Apply the power rule: goes to

      The result is:

    To find :

    1. Apply the power rule: goes to

    Now plug in to the quotient rule:

  2. Now simplify:


The answer is:

The graph
The first derivative [src]
    / 3    \      2
  2*\x  + 4/   3*x 
- ---------- + ----
       3         2 
      x         x  
$$\frac{3 x^{2}}{x^{2}} - \frac{2 \left(x^{3} + 4\right)}{x^{3}}$$
The second derivative [src]
  /          3\
  |     4 + x |
6*|-1 + ------|
  |        3  |
  \       x   /
---------------
       x       
$$\frac{6 \left(-1 + \frac{x^{3} + 4}{x^{3}}\right)}{x}$$
The third derivative [src]
   /         3\
   |    4 + x |
24*|1 - ------|
   |       3  |
   \      x   /
---------------
        2      
       x       
$$\frac{24 \cdot \left(1 - \frac{x^{3} + 4}{x^{3}}\right)}{x^{2}}$$
The graph
Derivative of (x^3+4)/(x^2)