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Derivative of:
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Graphing y =:
(x^3+4)/(x^2)
Identical expressions
(x^ three + four)/(x^ two)
(x cubed plus 4) divide by (x squared )
(x to the power of three plus four) divide by (x to the power of two)
(x3+4)/(x2)
x3+4/x2
(x³+4)/(x²)
(x to the power of 3+4)/(x to the power of 2)
x^3+4/x^2
(x^3+4) divide by (x^2)
Similar expressions
(x^3-4)/(x^2)

The derivative of the function/ (x^3+4)/(x^2)

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

The solution

You have entered [src]

 3    
x  + 4
------
   2  
  x

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

  / 3    \
d |x  + 4|
--|------|
dx|   2  |
  \  x   /

$$\frac{d}{d x} \frac{x^{3} + 4}{x^{2}}$$

Transform

Detail solution

Apply the quotient rule, which is:

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

$f{\left(x \right)} = x^{3} + 4$ and $g{\left(x \right)} = x^{2}$ .

To find $\frac{d}{d x} f{\left(x \right)}$ :
1. Differentiate $x^{3} + 4$ term by term:
  1. The derivative of the constant $4$ is zero.
  2. Apply the power rule: $x^{3}$ goes to $3 x^{2}$
  The result is: $3 x^{2}$
To find $\frac{d}{d x} g{\left(x \right)}$ :
1. Apply the power rule: $x^{2}$ goes to $2 x$
Now plug in to the quotient rule:

$\frac{3 x^{4} - 2 x \left(x^{3} + 4\right)}{x^{4}}$
Now simplify:

$1 - \frac{8}{x^{3}}$

The answer is:

$1 - \frac{8}{x^{3}}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

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

$$\frac{3 x^{2}}{x^{2}} - \frac{2 \left(x^{3} + 4\right)}{x^{3}}$$

Simplify

The second derivative [src]

  /          3\
  |     4 + x |
6*|-1 + ------|
  |        3  |
  \       x   /
---------------
       x

$$\frac{6 \left(-1 + \frac{x^{3} + 4}{x^{3}}\right)}{x}$$

Simplify

The third derivative [src]

   /         3\
   |    4 + x |
24*|1 - ------|
   |       3  |
   \      x   /
---------------
        2      
       x

$$\frac{24 \cdot \left(1 - \frac{x^{3} + 4}{x^{3}}\right)}{x^{2}}$$

Simplify

The graph

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